Cheap one-pickup electric guitar options
There's a funny thing about one-pickup electric guitars...
...and that funny thing is that for the most part, it's seen as a "custom shop only" thing. But you absolutely shouldn't have to pay several thousands of dollars just to have a one-pickup guitar.
The cheapest one-pickup electric I'm aware of is the Epiphone Les Paul Junior, seen above. This is a guitar priced at well under $200 at the time I write this.
The only other cheap one-pickup electric I knew of was the Kramer Baretta Special, but it was discontinued years ago. The Kramer Baretta is still made, but it's not cheap like the Special was.
Is there anything besides the Epi LP Junior for a cheap one-pickup electric? There may not be. Sure, you can find one-pickup guitars made for kids, but the Junior may stand alone as the only cheap adult size one-pickup electric.
Why would anyone want a one-pickup electric guitar?
There are some guitar players who only use the bridge pickup. That rear pickup is where they live. The front neck pickup isn't used. Ever.
People who only use the bridge pickup on an electric will sometimes physically cut the wires and take out the front pickup to allow for easier play. When no neck pickup is present, a player who plays in that area won't constantly be hitting the pickup with a pick.
What is the easiest way to get a one-pickup guitar for cheap?
Take a guitar with 2 or 3 pickups and convert it to just one.
Get a guitar where most or all of the electronics are mounted in a pick guard, then just swap out the pick guard for one where the other pickup locations aren't present.
The easiest guitars to convert over to one-pickup are Stratocasters and Telecasters (even if not made by Fender or Squier) because a) there are so many of them out there, and b) because the pick guard conversions are available inexpensively right now.
Esquire pick guards are dirt cheap and is arguably the easiest one-pickup conversion to do. The Telecaster and Esquire look identical to each other, save for the fact the Esquire does not have a neck pickup.
And yes, technically the Esquire has different pickup wiring compared to a Telecaster, but if you don't bother with the Esquire wiring, nobody is going to notice.
Stratocaster single-humbucker conversion
This conversion requires slightly more work, because if converting from 3 singles to 1 humbucker, the volume pot needs to be changed from 250K to 500K (otherwise there won't be enough treble response out of the humbucker and it will sound "muddy".) Fortunately, one 500K volume pot is cheap to buy.
Other guitars without pick guards?
The above guitar, a cheap Ibanez GRX70, does not have a pick guard.
If you convert over one of these to a single pickup and take out the other 2, what you're left with are ugly holes.
How can you make those empty holes look better? Fill the holes with black foam. Get yourself a pack of black foam sheets, cut the foam to the size of the pickup cavity and use as many layers as needed until the hole is filled.
Yes, there is white foam available, but I don't recommend using it. In a very short period of time, that foam will start discoloring and turn brown just from regular play and there's really no way around that. Black foam is a much better choice, even if the guitar you convert over to a single pickup is a lighter color.