My ice maker will work great for a while, maybe a month or so, & then stop working. It may not work for a week or so and then out of the blue, it starts working again. Hotpoint side by side, about 12 -13 years old.

Good day,
I will assume that the freezer maintains it's normal temperature.
If the temperature in the freezer rises much above 10 degrees the ice maker will lock out. That is by design.
There are 2 possibilities. One is the water valve located in the bottom rear of the machine. Any water valve over 5 years of age is suspect. They will at times refuse to open when the ice maker tells it to, and can become erratic.

If replacing it fails to solve the problem, then unfortunately you will need to repace the ice maker, which at that age would not be abnormal.

If you do the water valve first, and need to follow up with the icemaker itself, nothing is really lost since it is standard proceedure to replace the valve if a new icemaker is installed.