Reddit mentions of Leviton 9875 Porcelain Outlet Box Mount, Incandescent Ceiling Lampholder, Keyless, White

It's hard to tell from your photo, but the old-style light bulb socket might be a good bet here. It seems like if you take out the bracket you can screw this directly to the box.

Firstly before anything. Cut the power to that line. Via the switch in the wall, or better yet at the panel.

You can buy a power ticker really cheap to test to see if its live.

Honestly buying a light like this is cake to install.

Just attach the grounds(Copper wires) together, cap them and electrical tape the cap if you wanna get serious. Then attach the neutrals (white wires), cap and tape them. Finnally the hot(black wires), cap and tape.

Screw the lighting fixture to the box. And bingo.

Then just turn the power back on at the panel and screw in a lightbulb.

chain of low wattage halogen bulbs is what I use in my arboreal monitor lizard enclosure. 8 of them total wired in pairs. You will probably need 4-5.

Few benefits to this setup: you can individually dim each pair to fine tune temperature. You can individually replace bulbs in each pair to fine tune even more(for summer I replace some with low heat leds). You can also automate each pair to go on/off at certain time to emulate dusk/dawn. Chain of lower wattage lights doesn't affect humidity as much.

Here is how it looks in my enclosure. It is evening, so most of the lights are off for the night.

All you need for that is piece of plywood, number of inexpensive ceramic lamp holders, and 35 watt lensed flood halogen bulbs.

I bought two of those for about 10$ each at the grocery store. I was skeptic at first of their "100w equivalent output", but they give out as much light as the 150w incandescents I was using before. I then bought a box of 4 "60w equivalent" to replace some 100w lights. I also replaced the shitty light fixture in the bathroom in which whatever bulb I tried wasn't working except for the shitty CFLs that were in it when I moved in. A motherfucking porcelain socket with a "60w" LED bulb already lights my tiny bathroom better. I think if I replace it with a "100w", it will be perfect.

If you already dabble in home automation or want to get started, you could hard-wire this type of fixture each of them, then install this recessed z-wave sensor. In this case you'd also need to get smart bulbs (I like Osram LIGHTIFY bulbs. You can get on/off only ones for $20). Then you'd configure your hub to turn on the lights every time the contact opens, and turn them off when it closes.