I experienced that stumble in a 172H ('67) at about 7000 msl forgetting
to switch to a single tank on a moderate temperature climbout.

Our theory was intially a vaporlock in the fuel lines even though this
was in the days before autofuel. It quit completely with no warning
for maybe about 20 seconds & then came to life normally. We had
switched to single tanks and pulled the inside fuel drain at the same
time. Maybe if we'd done nothing it would have recovered as well. To
this day I don't know what made it quit.

There was another poster maybe a year ago suggested a fuel vent
problem. He may well be right. Cessna was unable to simulate the
problem but they added both front and rear down pipes to each fuel tank
in later years.

I wouldn't switch the fuel selector before runup since you have to take
off and land on both. Try them individually enroute unless you are on
an extended over water flight. Make sure on the ground every annual
that it will shut off though.

Personally since I use autofuel in a 172M now, I turn the fuel off
taxiing in so that the carb bowl is parked empty & then gets fresh fuel
to aid cold startups. Makes the starting much easier & more
predictable. The primer won't work with the fuel shut off.