Just went to a friends house that has a now broken Tri-Zone.
I may have solved this while typing this question but just in case here goes.
When the F2 fuse is replaced and the game is powered up, the machine will immediately serve up a ball without pushing the start button and the F2 fuse blows quickly.
I was able to get his schematics and see that this fuse is linked to the coils. I tested every one of the coils, (or so I thought), and they all read 4.4 on my meter.
However now that I am home I realize I forgot to test the coil that is under the apron that deliverers the ball to the shooter lane.
Since the machine is serving up a ball immediately at power up, I am now thinking this may be the shorted coil and I feel like an idiot for forgetting about it.
I realize it could also be a bad transistor on the board, but thought I would post here in case any of you had some more ideas to try as I am not the best person for pins from the 80's.

Thanks Loyd. Just the kind of good info I need.

Well, it is not my machine and even though I offered to try and replace some transistors the owner feels the board has more problems and is going to get this $199 replacement.
I will post back if he gets it and it works well.
http://www.pinballpcb.com/System3-7DriverBoard.html

I know that Mad Amusements has the two boards combined for $279 but he is trying not to spend too much. It would be nice not to have to worry about that interconnect section between the two boards.