It's possible the water pressure valve itself could be bad. I'd check that first as its the cheapest and easiest fix. How much is it fluctuating? Like constant low/high? Does it fluctuate and then stays low? Have you been in the room with the valve to watch it click on and off while the water is running? If its clicking on and off a lot, there's a chance its gone bad. You can turn the power off, take off the protective cover and look at the contacts. If you see some slight charring or discoloration, it might be having issues and needs to be replaced. Also, sometimes the metal nipple it sits on can get plugged up with rust/silt. You have to unscrew the switch from it (power off) and look down inside to see, but its a simple fix if you do it yourself.
Next would be to check the tank itself. It's possible the bladder inside is ruptured (worn out) and has become water logged. If this has happened, you'll probably have more low water pressure than the symptoms you currently have until you get no water at all. This should be a rather easy check. Just gently rock the tank back and forth. If its full or near full, its gone bad.
If its the pump, it'll have the symptoms (really all 3 have those symptoms to start with) but like the tank issue, you'll end up with no water at all once the pump finally gives up. Typically with a pump going bad you might see issues starting before major symptoms. Like spells of low pressure. Maybe no water at all for a few seconds and then everything is fine. It's basically warning you its about to give up. How old is it? If its been there 20 years or so, it's likely that (especially if the other two check out ok). Even if its not, you should probably look into getting a new one because they don't last much longer than that. 25 years on the higher end so depending on your finances, you could milk it for awhile longer if you need to.
And while I assume you ruled everything else out to get to these 3, I just want to make sure because some people overlook stuff that's a real simple fix. If you have a whole house water filter, check the filter, replace it with a clean one and bleed the lines properly (can take several minutes). If you don't have one (or even if you do), check the aerators on the faucets. You can unscrew them by hand or an adjustable wrench. Clean them out. Though if you're getting pressure issues on bath tubs and toilets, it won't be a faucet aerator issue. Lastly, just visibly inspect everywhere on your property where you know the lines are to see if you notice any signs of a leak.
All good advice.
I would add the 'Control Box' into the possible problem.
I had similar issues as OP with low pressure on a 40/60 switch, faucets sputtering, and even my washing machine giving me low water pressure alarms.
First thing I did was shut the power off to the system and drained the tank. I checked the air pressure on the empty tank with a tire gauge and it read 38 lbs where it was supposed to. Basically 2 lbs lower than the low on the 40/60 pressure switch.
Turned the power back on and let the tank fill back up. Once filled I shut the power back off and adjusted the spring down on the pressure switch a couple turns in attempt to increase pressure and it didn't change anything. Looked at the contacts and one side were charred. Bought a new pressure switch ($20), installed and got back to 60 lbs.
However, there were still issues with the pump cutting off at 60 lbs. Just a long low pitch hum noise for a few minutes.
Since I knew I now had a good switch, the next step was the Control Box.
The Control Box has 2 big capacitors and a relay up inside that you can't see unless you take the cover off. (BTW the cover has to be on the Control Box
and closed for it to work.)
Anyway one of the capacitors in the control box was discolored. I could have ordered the capacitor but opted to just buy a new control box ($245). Either the pressure switch damaged the control box or vice versa.
Basically power from the breaker panel, to the pressure switch, to the control box, to the pump.
Also of note, some control boxes have two reset buttons located on the bottom of the box. They'll pop in a power surge and just need to be pushed to reset.
All good now. Pump on at 40 lbs, and off at 60 lbs.