This is for the light for my house number. The light bulbs burned out and I'm trying to figure out how to replace them. I tried to pull the bulbs out but it didn't budge. Perhaps I didn't pull hard enough but I'm wondering if I need to unscrew something to release the bulb.
So my questions are:
As @RMDman suggested, those are lower voltage bulbs. A type 194 bulb designed for automotive 12V DC systems looks like this:
and a modern LED version may look more like this:
With LED versions, many send light out the end in a cone rather than radiating in all directions. The pictured LED version has emitters for all directions, but may be too bright for your application. It may be easier and give more uniform light just to go with an old-school "long life" bulb. Such bulbs should also work with lower-than-spec voltage unlike LED bulbs.
Before choosing a replacement bulb, use a multimeter to determine the voltage supplied across the white wires to your bulb mount, and whether it is AC or DC. Your fixture looks like it has the bulbs in series, so each bulb would get 1/2 the voltage measured between the two white supply wires. As others have noted, LED bulbs may have polarity issues if it's DC, and may not work right on AC.
Edit: Found this view of a related socket showing what the inside of your sockets probably look like:
That does not look like it is attached to a junction box and the wiring attachments tell me it is low voltage. The bulbs are probably 194 12V and push in. So you need to pull them out. They may be somewhat corroded, so it may take some force.
The wiring looks rather like they're connected in series, meaning that one bulb failing will stop any light from being produced. You may only need to replace one, but if you do, it needs to be rated to the same power, as well as voltage, as the surviving one. Such cheap automotive bulbs often come in packs of 2 anyway
These bulbs can take quite a bit of force to remove, but you can't grab them with a tool or you'll break the glass. Latex gloves are good for increasing your grip and giving a tiny bit of protection against shards if they break.
If they're completely stuck, you should be able to get new bases. They may not be a direct replacement but there are screw-in low voltage bases as well as ones intended for use in cars. At that point it would be worth measuring the voltage (and whether it's AC or DC) and considering whether series or parallel connection is more appropriate.
Personally, if a simple bulb replacement wasn't going to happen, I'd build my own LED illumination, with rectifiers if necessary and appropriate resistors.
Enlarging the bulb and socket shows the labelling Christiana 9000 and the internet seems to have various hits on that. As well as a plethora of "you know, maybe, maybe not, ha-ha, if we drop things from your search term" hits. Both bulbs and sockets seems to be the definition of inexpensive. Of course, having to replace the sockets would make the overall job more involved than just working the bulbs free and putting in new ones.
Definitely pull out, straight out. If you wiggle it/one to free up any stickiness/reluctance, do it left-right so to speak, on its axis that is parallel to the plane of the plate they are mounted on. Also, remember counter-torque and adequately hold the socket itself still as you work the bulb.
Might also point out that the wires are barely connected, which isn't a thing if you did that yourself before taking the photo. But if they were like that, you'd probably want to improve it to some extent. At least clean the connectors and wire ends before putting them back in the incredibly sad way they are now. But, you know, no preaching here. If they lasted a long, long time prior to this, they may do so again, sad connection or not, and the voltage is in the "safe" zone, so...
A tighter connection, even some solder, might make the next set of bulbs last longer and perform better while doing so.
They look like small halogen bulbs. Replacement versions that use LEDs (less power, but more importantly last longer) are available for many sizes.
Pull them straight out - i.e., left for the one of the left, right for the one on the right. Then get a close-in picture of the numbers on the bulbs to figure out exactly what they are to get the right replacements.
