When is homemade wine-based vinegar simply bad wine?
There is not really a turning point. The way that wine goes bad is the process of making vinegar. From wikipedia:

The word "vinegar" derives from the Old French vin aigre, meaning "sour wine".

The Canadian government limits things that can be sold as 'vinegar' to something with an acetic acid content of 4-12%, so you could do the technical-bureaucratic thing and wait for the acetic acid to get up to 4%.

If you aren't hung up on technicalities, then you can  use it as soon as it gets sour enough. It is done when all the alcohol has been changed to acetic acid, but it is a bit hard to taste since the acetic flavor dominates.