I'm not an auto repair expert so I'm looking for advice. I've got a 1987 244 DL that's had some issues starting up.

Two weeks ago I'd try to start the car, it would attempt to start but just not catch on the first attempt, then turn over on the second attempt. Several days later it would take three to four attempts before turning over, then it just wouldn't turn. Even though the battery had juice I had a friend help me jump it and it started up. After letting the car run for 15 minutes then turning the car off I tried to start it again and it wouldn't turn over and the battery now seemed weak. After a third attempt to start the car the battery was dead.

I replaced the battery figuring it was pretty old and with the new battery the car would start up on the first attempt for a week. Then all of a sudden it took six tries before it would turn over, then after turning it off and trying to turn it over again it just wouldn't turn over. A friend noticed there was no smell of gas near the engine, so we figured on a fuel delivery problem, so he listened at the gas cap and couldn't hear the fuel pump doing anything. We opened the trunk, peeled back the carpet and removed the plate covering the fuel pump and still heard nothing when turning the key to the accessories mode or when trying to start it.

Now I'm pretty poor at troubleshooting electrical stuff but we took a voltage tester that was just a thing with a bulb attached and attached it to the wiring just before it went into the fuel pump (jiggling / moving the wires around a bit first) and got a light, and then I tried turning over the car and it turns over fine and has continued to start up right away all day.

I'm thinking out loud here but I assume fuel pumps either work or they don't so I'm ruling out a fuel pump issue. I suspect it's an intermittent problem with the fuel pump relay and I should replace it (since it's inexpensive) to play it safe and keep this problem from happening again.

Does this sound like the right course of action to anyone, or is it more likely to be a poor/loose wiring issue, or am I completely missing something? And I should add that I checked the fuses and all look fine.

Thanks for any advice!
Tom