On most motion detectors, you can flip the switch on and off rapidly to override the motion detector function. You'll have to check the owners manual.

"help support" is not nearly the same as "firmly bond to" and if you have ever compared the strength of the two, it's easy to crack off the excess Great Stuff foam, but I've never been able to crack epoxy without using massive quantities of leverage. Plus this will be outside, and UV radiation from sunlight massively degrades polyurethane foam, so that's another reason I would vote against it.

Epoxy does get hot when curing, but I doubt it's hot enough to start a fire. The rebar would act as a heatsink regardless.

I still think epoxy is a better choice, because it needs to bond to both metal and wood, and I don't think Titebond grabs well onto metal.

Go to a boating supply store like West Marine. You can buy one gallon and two gallon buckets of two-part epoxy. It's not cheap.

You can also order it from Amazon, I would think.

Why not use the rebar in a slightly oversized hole, and then pour epoxy down the hole?

This will lock the wood to the rebar, and also prevent the rebar from working it's way out of the wood. And even if the wood did somehow rot away, the rebar would be encased in a "tube" of epoxy and be unable to damage anyone.

Or robot slaves. Damnit slave, get back out there and keep washing the car!

For something that old, it's almost impossible to get an exact replacement for a motor like that. You can sometimes find something that fits, but then the rpm's and stuff won't be right. If you find something that has the right rpms, the mounting brackets won't be in the right place.

First thing I'd do is just clean it up enough to see where the screws are to remove the motor casing. Sometimes inexpensive motors were riveted, so you'll have to drill out the rivets.

Then replace the cord and see if it works. If not, you can rebuild it, it's not too hard, just watch a youtube channel called Linguoer, she lives in China and rebuilds motors with only basic tools. It doesn't look that hard.

Or you could find a motor repair shop, they are usually pretty common, people take their pool pump motors there to be rebuilt. Just ask at the pool supply store and they'll know who is the best in town.