FWIW my mutlimeter is a Aidetek VC99+ and it's great (and affordable). I've just noticed it has a Hz setting, not sure if that will check pwm pulsing for rpm, however I have hooked it up to the lamptron to log the DC volts and it does seem to show the average V when the unit is supplying pwm signal to the fan. You get a bit of a drift +/-0.5V but it's easy enough to work out the net average.
I can't see it on there anymore but this one looks nigh-on identical:
https://www.amazon.co.uk/Auto-Rangin...dp/B00EYYJRC0/
Give me the evening and I'll have a play re the pwm/rpm side of things. Not sure if it will play ball only having one lead connected though to the pwm header pin. Maybe the 2nd lead just needs to go to ground idk?