The classic way to test a transom is to pull down (or jump on) the prop of a tilted motor. Should not move at all. More than 1/2 inch is a problem.
For a temp solution, you can inject "thinned epoxy" such as CPES or git rot. I got the 2 gallon kit, but the next size down may be enough, plus syringes, and the small sized west systems epoxy kit.
How handy are you with epoxy? Injecting takes a day or two, and it's not too hard.
*Obviously, the best thing is to pull the motor and redo the transom. And from experience I can tell you that if you inject epoxy now you will make life hard for whoever decided to redo the transom later. From my experience, immensely harder.
1. Start by drilling a few 1/8" holes at the bottom and top of the transom. Angle them downward on the top, and only drill through one side of the transom (i.e. either inside skin or outside skin, not both). Hopefully no water comes out.
If the wood is sopping wet...
2. Use a 60cc syringe to inject acetone into the top holes until you see it "weep" out of the bottom holes.
3. Wait a day or two for the acetone to dry. Apparently you can dry with a hair drier or air gun, but I waited a day to be safe.
If the wood is not wet, or once it is dry:
4. Mix up the CPES and start injecting into the top holes.
5. Once the CPES starts weeping from the bottom holes, plug them. I used a dowel sanded into a cone/point.
6. Keep injecting, go from one hole to the next, you will be amazed at how much volume you end up injecting. Also, don't go too fast.
7. Eventually, the wood will be saturated.
8.
Bake@350 degrees for 3 hours or until skin is lightly brown and toasted. Just kidding. Takes about a day for the CPES to set up.
AFTER CPES CURES
9 Drill out all holes, and fill with epoxy/fillet.
10. paint.
11. For the alum stuff, I would just use 5200.
AGAIN, I ADVISED REDOING THE WHOLE TRANSOM, NOT INJECTING, from personal experience.