Don't damage the pins for the fuse or other terminals front probing with a meter. We use terminal test tools that are the exact male terminal that corresponds to the female terminal.
I also have an amp clamp with a BNC connector to hook it to a scope. There are also clamps with a display built in.
Or use a meter, but a cheap meter may not be very accurate or even work at all. I had to cough up the $400 for a Fluke to do accurate parasitic battery drains.
If you do use a meter, yeah, maybe do it between the connector at each fuel pump. Backprobe if possible. Or find a way to avoid terminal damage. These old Volvos have overbuilt terminals, but if you front probe on a modern car it's very easy to damage the tiny terminals. If you have to, use a needle probe. They even come with 4mm banana terminals to connect to meter leads. Or go raid grandma's sewing kit and get some of those "T" needles and use alligator clips connected to them.
Here is a waveform of the main fuel pump on my 1990 240. This was about 2 years ago. It's not as pretty as I would like. With graphing the waveform you can see each of the 8 commutator current humps and also the average current draw. Since this pic, my 1990 240 knocks on accel and fuel pump is also getting loud. It may be dying. I am curious to see what the current waveform looks like now. It looks like I was around 2 amps in this pic. (Tough to see. I know. Sry.)
In your case, consider checking the fuse connections and crimps. Grounds and terminal connections and under car wiring too. Bad wiring can cause excess resistance and heat and cause components to fail. Such as blower motors pulling too much current, then causing the resistor to overheat and fail. A new resistor will fix it, but fail soon.