That’s the idea, it seems to reach a tipping point where it goes from thinned to pretty useless quite quickly, so when it gets towards what you’re looking for, slow down with the thinner to a drop or two at a time
Thinned filler keeps just fine in a sealed paint jar.
Keep in mind that adding thinner can make the filler “hotter” than it previously was, so using it to fill any deep gaps may melt / deform the surrounding plastic - I tend to keep it for smaller repairs or for finishing larger repairs. It will also shrink more than it did before thinning, which is another reason for not using it on deep repairs.
On the other hand, especially if you mask off the area surrounding the area you’re filling, you can thin the putty to about the consistency of thick paint and brush it on one layer at a time, allowing it to dry before applying the next layer. You can then over-fill the area to the thickness of the tape around it, remove the tape and have what is essentially a paper-thin, relatively smooth layer of putty, which is dead easy to wet-sand with a fine-grit wet and dry.
I’ve tried a few different things to thin (Squadron) putty. Regular hardware store lacquer thinner, Testors “pink” label liquid cement, Tamiya lacquer thinner. When applied thinly as I described previously, the solvent usually evaporates before it damages the plastic.