For most "continuity" checks, 100 ohms equals an open circuit. At least if one is tracing out wires, or traces on a circuit board. At least in the checking that I have done. That was the advantage of the incandescent lamp checker, which was flowing a bit of current thru the wire. About 0.150 Amps, to be exact.

 

Was just making the point that the circuit (or wire if long enough) can read open. But pump 240VAC down that line and you could have some excitement. That's why I suggested using a DMM.

 

What is missing here is a specification of both the maximum acceptable resistance value that can be accepted as OK continuity, and a spec of what current the tested circuit must be good for. It does matter.
And a tester that has a light that is on when not testing will soon have a drained battery. So what benefit does the TS believe that light will provide??

 

a tester that has a light that is on when not testing will soon have a drained battery.

Not with a push button. Or maybe it should be called "Push To Test". Battery is active only when the PB is pressed. A switch may be more convenient but it can be left on inadvertently. That's why my initial thought is to use a PB. If you REALLY want to get fancy you can incorporate a PB into the probe so that when you apply pressure with the tip it pushes the button.

 

I have one of these:
https://www.amazon.com/Bussmann-FT-3-Automotive-Tester-Puller/dp/B00139OH0G/ref=asc_df_B00139OH0G

It lights up if the fuse is good. And ONLY lights up when there's a good fuse (or continuity).