82 international Bad starter?

I think your assessment is correct. Starter solenoid. IF you can direct jump from your battery to starter without key on. Or use a screw driver and short your starter terminals.You should hear your solenoid kick.
IF not its bad. You can just replace the solenoid. I have always replaced whole unit when needed.
I now have a high torque starter and I like it. Its lighter and needs less energy to crank motor.
Pulling starter off is easy. 3 bolts and a few wires. Disconnect batteries first and remember where the wires connect. I use a cable tie and put thru eyelets to keep them together.
Good luck

 

You could also just have corroded terminals. Just clean them and tighten back up, before you remove anything.

 

If the batteries failed the load test, they'll have to be replaced anyways. I'd start with that. Usually if the batteries are low on charge, you'll hear a high rate clicking of the solenoid cycling. If the starter turns but won't engage the flywheel, the solenoid is closing the contacts like it should but the pinion is either not engaging the flywheel, or you could have a damaged starter pinion or ring gear teeth.

 

Did replacing batteries fix your problem