Engine Light - Gas Cap issue with incompletely filling tank

I have a 2003 Jeep Liberty Sport with 44,000 miles on it. My engine light has been going on and off (not blinking) for several thousand miles. I had it checked once and they said it was the gas cap and they reset it. It stayed off for a short while and then came back on. I recently filled up my tank completely for the first time in awhile and the engine light is now off. Was wondering if not filling up the tank (1/2 to 3/4) can cause the engine light to come on in regards to the gas cap. I’ll try filling the tank a couple of times and see if it stays off.

Cleaning the cap and neck would be try one, just a paper towel will do, new gas cap might be inexpensive fix two to try, I do not know about this model but 1 Chrysler product we had used a pump every xx miles to pressurize and test the system, the pump failed, the dealer did a reset and the light was on the next day again. The new pump fixed the problem.