I presume that you do not have a CSV for what I write next.
I have a 30/50 Pumptrol pressure switch on a 20 gallon pressure tank for my well. The pressure gauge reading on the tank stays at around 58 psi when the pump is not in use. Once I ran the the faucet, it took about 2 minutes and 51 seconds before the gauge dropped from 58 psi down to around 29 psi. Around the last second before the pressure switch turned the pump back on, the gauge's needle dropped rapidly from 40 to 29 psi and then jumped back rapidly to 40 psi before slowly rising the pressure on the gauge.
I suspect that pressure switch has been turned up to around 40/60.
It then took the pressure switch 2 minutes to rise back to 58 psi before turning off. Is this normal?
I agree you need a new tank. But there is something else; with a good tank, it would take about 5 gallons to go from 40 psi to 58 psi. Was there water being used during those two minutes? If not your pump would seem to be working on the edge -- barely being able to get to 58 psi. So maybe, in addition to replacing the pressure tank, you might consider dropping the pressure switch setting a bit, maybe 35/55, to give yourself some margin. On the other hand, if you have a CSV, then the pressure rising slowly as your pressure switch approaches cutoff is normal.
What is your pump? In MN, I would usually presume it was submersible.