I own a 1987 Volvo 240 GL and have had it for about 2 months now. I live in Hawaii so there's not a whole lot of options as far as 240s go, and I had seen an ad for a very good condition one not too far from my house. Before I got the car I was waiting for "the fuel pump" (their words) to be replaced as the car had a no-start condition. I never saw the car failing to start though so from what I learned later I have no clue what was causing that to happen, if it was happening at all..
When I asked which pump it was they said it was the secondary fuel pump and also the sock filter (the in-tank one). Having owned a 240 before, I knew that the car would still run without it functioning so I dismissed it as a case of them not knowing the car too well. Anyway that's it for the backstory, I've never had an issue with the car not starting but after buying the car there was a strange case of severe hesitation whenever I tried to accelerate. It would only happen if it was hot outside (never happened early in the morning or late at night) and when I eventually got up to speed the car would be fine until I had to stop and then start accelerating again. The hesitation is hard to describe but the engine RPM would get to about 1,750 before dipping well below idle speed and then shooting back up again. It would repeat that cycle in rapid succession maybe 4 or 5 times before I eventually got going. If I was going uphill, even the slightest of inclines, and accelerating there was a chance the car would quit altogether and wouldn't restart until it was back on level ground.
After a lot of diagnosing and thinking about the only repair i was aware of, I decided to unplug the power for the in-tank fuel pump (which I was pretty sure wasn't even functioning anymore as I couldn't hear it)
As soon as the pump was unplugged the car would run perfectly fine. I can stop mid-drive and plug it back in to cause the problem again. Where I've disconnected it is in the trunk under the plastic panel/cover on the left side, it's a yellow/red wire running into a black one (sedan trunk).
I've been running the car with the in-tank pump disabled but I would like to fix it before the main pump decides to give up altogether. The strain put on it can (and will) cause premature failure. If I do figure out the issue, I will replace the main pump because I don't trust it too much.

Something to note is that I did test the fuel pump relay and eventually replaced it and the condition still persisted. I am very confident that I've isolated the issue to the secondary pump and was wondering about actions to take next.

I have wanted to open up the fuel tank and check the pump myself but I have been very busy and haven't done many repairs (voluntarily, at least..water pump broke a week ago but that's a story for another day).
When I do get around to opening it up, is there anything in particular i should be looking for? I have a digital multimeter so I can test the pump that way as well.


Yes I did check the forum and I did see a very similar case to mine with very similar symptoms, but it seems they solved the problem by running the tank empty and refilling with good gas. I've run the tank to empty before and the problem is solved by unplugging a wire (which shouldn't magically change the condition of the gas)

I appreciate any and all help, this is the first time I've resorted to asking a forum directly because my situation is so specific that I wouldn't even know how to look it up like all the other repairs I've done.