If you "must" know hi-hi-Z points like Fender longtail grids...
There are ways. Real high precision needs some complexity.
But for the accuracy you need in tube-work, and the speed you (don't) need for DIY, this will work good enough.
It takes power from the amp being tested.
It reads 2V-3V low, a factor of the specific MOSFET you get, temperature, some other slop. So before you read a grid, read a nearby point which can be measured with DMM and with this buffer and DMM. In the longtail, the cathodes are an obvious point. They don't sag (much) when you poke a DMM at them, and they are very near grid voltage which keeps other errors small.
Say the cathodes read 80V on DMM, and 77.5V with buffer between cathodes and DMM. So it reads 2.5V low, in this voltage range, today.
Now poke the grid with the buffer and read the DMM. Say it reads 75.5V. But you know the buffer reads 2.5V low. So the true grid voltage is 78V.
Oh: if the Gate+10Meg is not connected to anything, the DMM reading is completely random. The ultra high Gate impedance may hold the last voltage it saw for many seconds, or drift up or down to any other voltage. It only is valid when connected to something.
High-high-Z work is painstaking. The least dirt or moisture spoils the reading. In this case, the Gate pin, the 10Meg, and the wire to the grid being tested, must have LOW leakage to anything. Don't put these critical points on terminals, especially cheap phenolic. I would epoxy the MOSFET to a board or chassis (the tab is electrically "live"; gluing face-down is valid), keeping epoxy off the gate lead area. Solder the 10Meg right to the MOSFET Gate leg (no, you can not hurt the MOSFET with solder). Trim the leads, solder a good insulated clip wire to the other end of the 10Meg. None of this should touch anything! Air is your best friend. Wash around the gate leg with fresh rubbing alcohol, dry over a hot lamp.
The 10K, 220K, and meter-point can be on perfboard etc, though I would be tempted to solder right on the MOSFET, then shrink-tube the contraption so the tab and legs can't short to stuff. Clipleads will let you connect to B+ (not plate!) and ground and DMM.