You are mixing two markedly different advice streams.
To quickly find a short, with your minimal electrical knowledge, is what I proposed.
Unplug all the wires in the headlight.
Put the fuse in place.
Plug things in one by one. The "snap" sound will provide audible report when you get the faulty device.
Once you've zero'ed in on it you can either: visually see the defect, or, in the case of the switch being internally shorted, prove it with your DMM.
Repair/replace the fault.
As you said previously... His issue is a shorted connection.
He's either got a misplaced wire connected to his switch that grounds when he turns the switch to the off position, or a skinned wire that connects to ground when he throws the switch. It's also possible that he's got a bare wire touching the inside of his headlight shell, which is a common issue with dead shorts. So he needs to heat shrink everything that's bare inside the headlight shell if there's any wonder that a bare wire might touch the inside of the shell.
He needs to find the problematic connection, which is a misplaced continuity to ground (a short)...... and instead he's measuring resistance of connections
You should be searching for a short..... so reconnect everything, put the tester in place of the battery terminals, set to the continuity setting, turn the key on and the switch off. The tone should be sounding. Now start disconnecting things until the tone goes off... When it goes off, you are on the circuit that is grounding out and need to follow it to double check it's proper connection status, and look for any skinned parts of the wire that might be touching ground.....
At no point does the exact amount of resistance matter.... it's continuity to ground (a short circuit) that is your problem...
*** also, so you turn on the key switch and you'll get a tone from the ignition circuit. Maybe pull the ignition wire from the key switch so you're only left with "switched" circuits left to test.... Those being the light circuits, directionals, brake lights, running lights, headlamps. If the tone goes off when you switch them off then they are not part of the shorting problem... (From what you said originally, the problem is in the main headlight switch circuitry)