The trouble with "hacking" a continuity tester is the output voltage. Are you looking to put a new stake in, or are you measuring an existing stake?
from the friend's description... he want to measure existing building ground connection to earth. from the above video, there are 3 wires coming out of measurement device (Kewtech), one goes to earth electrode, 2 probes go to stakes buried few feet apart by his colleagues, i guess that 2 stakes is for "earth reference" in the measurement setup, i'm not sure though why 2 instead of only 1 stake. as they measured it, the guy keep punching the 1st earth electrode until resistance measurement within acceptable range ie below 200.
so in my friend's case, i believe he is going to measure existing earth installation in a building, to ensure the earth resistance to building electrical wiring (ground wires) will be in compliance to some standard, or within some acceptable value.
checking the DET4TC, the applied voltage is 25-50V, but for insulation/continuity test, MIT310 is applying 250V-1KV. so i guess this whole thing is just a V = IR test, ie we apply V, measure the I, and hence we will get R. in both cases of continuity/insulation test and earth electrode test. am i correct? or wrong? what confuse me actually or i believe i still dont have a clear picture, is why the need of 2, 3 or more stakes needed to do the earth measurement? beside the earth electrode under test.