Sean, you want to put the cue so the change-over douser closes before all the ID tail crap runs through. All that extra stuff on the analog soundtrack can really raise hell with the speakers. Mine measures up about 12 feet or so from the last frame I want shown on the screen. Makes for a smoother shut-down.
So let's get the interlock out of the way. Thats NOT ever going to be your problem. Once a show is up and running on interlock it behaves exactly as it would in stand alone running. The only change being that the show's 'talk' to each other to start all and stop all in an alarm situation. Therefore interlock changes nothing.
I'll assume that the system in question has worked correctly at some point, or still does at times, and that the wiring has not been changed. If thats the case this is how it works.
Once an interval/end show cue has been seen the show will go into interval mode at the end of the preset time delay. The projector will continue running, waiting either for another cue to resume the show or the film to run out at the end of the feature. During this time the alarm system is turned off.
What is happening in your case is that the film sensors are not 'seeing' part of the tail runout and stopping the projector with film still in it. Either the tail runout is very dirty, you are placing some identification tape on the film or you are using an in house tail run out which is significantly duller than normal stock such that when it passes the sensors there is a significant drop in reflection. When this is run thru it is not 'seen' by the film sensors and the automation thinks the film has run out and stops the projector.
This is probably the case as you don't say you are having random shutdowns that you cannot explain. Therefore there is something different about the tail run outs.
Now it may also just be a case of a very dirty sensor assembly. They are easy to clean so that should be the first thing you try.
One other thing to check, which will tell you which sensor is not 'seeing' film.... Open up the TA10 and isolate one of the film sensors, presence or motion, and see how things go then. It's the two white dip switches on the main board about mid way up on the left.
With no film in the projector turn one of the switches off. Can't remeber which one is which but one of the green Led's on the top panel will illuminate to show either film motion or presence.
If it still happens with one then swap it and try again. Don't isolate both of them or the projector will not stop at all at the end of the show or if there is a film rupture during the show.
The TA10 works with events rather than simple do this now cue's so moving the pulse back or forward is not the issue. Even if the cue is in the wrong place the close may be untidy but it would still work as expected. Anything you're not sure about with the TA10 come back to me.
Hope this helps.
Nice to see you. Couldn't agree more with your assessment of the problem.
Thanks for the kind words about the products and your support.
Don Olson
dolson@componentengineering.com
can't knock a great product......
Kindest regards to you and your team.
I visited this booth for the first time today. (I have been to this theatre before on emergency calls, but never in this particular isolated booth).
Upon arriving, I tried Ken's suggestion of bypassing both film presence and film motion detectors with the switches. I started the automation, triggered a shut down cue and the automation acted as I would expect it too. That is, normal shut-down operation and the projector remained running until i shut off the detector by-pass switches. (This blew the theory I had about perhaps one the the event relay jumpers being long enough below the p.c.b. to touch ground on event 4 thus temprarily shorting out the power supply on the automation and thus knocking out the motor relay)
This would seem to give creedence to Ken's theory about the tail-piece (part of the feature, btw, not a house tail) being the problem.
My investigation ended here, however when i heard the squealing eminating from the sound head. Removing the 5-star cover, I discovered a badly worn idler roller and some belts in dire need of immediate replacement. The rest of my morning, unfortunately, was understandably devoted to obtaining and installing these parts before the first performance at noon.
More as I investigate further.
Since I disconnected them, the problem never returned.
The interlock cannot cause the problem in any way.
The only way the projector can be shut down WITHOUT an alarm sounding is if the film 'appears' to have run out after an interval cue, otherwise the alarms would sound.
This is clearly the case, there are no odd shutdowns and the system seems to be working correctly otherwise. I would suggest the next time you are there watch the end of the feature go thru.... keep an eye on the Motion and Presence led's and you will see one of them is flickering or going out, and that will stop the projecter.
Keep us posted.
In 45 years of electronic troubleshooting, I learned never to make a flat statement. 
There are no other unexplained faults, no shutdowns etc in all cases the system works perfectly. If the interlock wiring were at fault there would be all sorts of things going on. This problem is quite specific and clearly defined and is down to dirty sensors or dirty / dull tail runout.
Oh dear, all a bit heavy suddenly!

Gordon, I think I will put a switch in ours so we can use that option. With the very short shows, this option will be neat to have incorporated.
I put the film-motion overide switch on, to see if that was the problem. (There would still be fail-safe from the film-presence safety).
Today the projectionist reported normal shut-downs the rest of the day (i.e. the projector remained running until the film tailed out).
Couple of things I noticed. The film, as it leaves the last roller on the FM-35 goes down forward at about a 45-degree angle. I prefer more of an angle to get as much purchase on this fail-safe roller as possible, (to allow the film to lay quite flat as it passes the sensors). As it is, however, there have been no shutdowns during a performance.
The other thing i noticed was a generous length of very clear (no emulsion) tail on the end of the feature. This makes me wonder if it would be possible that while it might reflect light back to the presence failsafe, might it be clear enough not to give a square-wave signal of sufficient amplitude back for the motion failsafe.
In any event, I wish to thank you all for your advice and help. It is very much appreciated.
P.S Re-thinking this, it is obvious that if it is shiny enough to reflect back to the presence unit, it should also reflect back to the motion unit as well.
That's what I hate about electronic devices. When you think the propbem is nailed, something will happen to blow the theory right out the booth window.