I know the overdrive is working, because the engine slows down when I push the button. But when overdrive is OFF, the off light flashes on, and then goes off. Is there an ON indicator anywhere? Should the OFF light stay on?

Thanks very much. Glad to be a new member.

 

`When that light flashes , it usually is trying to tell you there may be a trans problem.

It might be a wise move to have your vehicle checked for any codes.They do not have to be trans codes.

 

Unclear. How long have you owned the van? Was it the very first time you ever pushed on that button?
When overdrive is OFF the indicator stays ON. If you shut off and restart your van overdrive will be in its default state, which is overdrive to be ON, thus the indicator will be OFF. And there is no such thing as indicator to be shown anywhere on your cluster when overdrive is OFF.
Go buy a Innova 3145 it can retrieve both engine and transmission codes, just not possible to retrieve abs codes. BTW, to retrieve abs codes (doesn't matter if yours is 94 OBD1 or 96 OBD2) if you have RABS (rear wheel drive) you need to ground the control wire to retrieve the flash codes, with 4WABS (4-wheel drive) you can't and you must use an abs capable scanner.
Once you get the code(s) post them here and additionally check my signature below and specify your engine size so I can provide you the pinpoint tests. Plus, check your transmission pan and count how many bolts.

You said "I know the overdrive is working, because the engine slows down when I push the button."
You've got the opposite. When you push that button overdrive is OFF.