Well, the good news is that you can easily replicate the problem. It sure beats having an intermittant problem
I think I would start by warming it up good, then checking EEC computer codes with a code reader, both Key ON, Engine OFF, and Key ON engine ON. I think this would be a good place to start, 'cuz the computer may already see something its not happy with, and that can save time and $ of guessing. But don't take the code as the gospel, as it can only make its code decisions on what it can see.
If you aren't familiar with the code reader for this pre-OBDII vehicle, it's a plug-in little adapter with an LED on it, comes with a manual, plugs into diagnostic connector usually under the hood on drivers side near firewall. It has instructions and they are pretty simple. Parts stores sell them, as does Sears in the tool area. About $35, I think.
That's what I would do first, before replacing any parts.