For minimal pull power I'd avoid going electric at all. Running large enough wires, etc. is going to be more work than I think 2k of pull would justify. I've got one of these that lives in my 80s tailgate storage and it is relatively safe and easy to use in situations where you just need a little bit of pull:
I've used the above with great effect in a variety of situations including when it's slick and traction is minimal or when I need side holding/pulling in an off-camber situation in combination with another/larger winch doing the primary pulling, etc. It's certainly a useful tool that is worth it's minimal weight and minimal complexity (no wiring). If you also have some appropriate tow straps and soft shackles then carefully work to drive within the limits of your recovery gear you can have a lightweight, no maintenance and low cost recovery kit that will get you out of some jambs. If you are rarely at risk of getting stuck the above may be all that's justified to carry around and it will at least keep you from a long wait to get recovered from a simple/minimal situation.
Hitch mounted winches have a lot of benefits and can be a great option but depending on how you set them up could easily be more complicated and/or expensive to build out than a typical stationary/front mount winch. While possibly having front and rear pull options could be great it's a lot more wiring, extra hitch, etc. to add to pull it off. On top of that, carrying the weight of a hitch mount setup to deploy it in off camber or slippery situations could be a real chore.
There are also gas powered capstans, etc. but they are typically not large enough to warrant their extra complexity and I don't consider capstans to be as safe as the more common spool winches or "comealongs" like linked to above.
Finally, for what you describe in your og post you can just get a 2k winch (like the Badlands trailer winch) for cheap but I really don't see the point in mounting and wiring one of those in on an 80 personally.