90 Toyota PU w/auto trans. starter say ingaged and is energized with key off.

 

"stay engaged"?

Welcome to YotaTech (you'll really help yourself if you proof-read your posts before sending them on.)

The starter is engaged by 12v on the solenoid lead. The solenoid lead is powered by the starting relay. The starting relay is in different places by year (and earlier models have no relay at all), but here's a photo of my '94. (in the junction box under the hood) Pin 3 goes to the starter.

Start by removing the relay. If the starter stays engaged, you have a stuck solenoid (or a solenoid wire shorted to 12v somewhere). If removing the relay releases the solenoid, you either have a stuck relay or stuck ignition switch. Use your multimeter to check for voltage on pins 1 and 2 (one goes to ground, the other to the ignition switch). That will tell you where the problem is.

In case this isn't clear, do not try to fix this without a multimeter. You'll be wasting your time (and ours). There is no excuse to not have one. https://www.harborfreight.com/7-func...ter-90899.html