break in continuity when test gas sending unit

Well it's "simple" the thing has problems. This is just a simple wirewound rheostat, that is a moving contact arm sliding across a coiled resistance wire.

So any poor contact in the moving part due to loose, rust, wear, corrosion, loss of arm tension, whatever will cause a problem

First tho, LOL make darn sure your ohmeter leads are making GOOD contact. I always use alligator clips.