You say it has a single contact on the base, right. Are the pins on the side horizontal or are they offset? I would think that they are horizontal. If you want to experiment with LEDs and you really want to screw up your brain let me start mixing you up. The base style would be a BA15S (15mm in diameter and single contact). One other style could be a BA9S (9mm in diameter and a single contact). Either with horizontal pins on the side. To select a LED you want to check the color. The white LEDs will be a wave length between 4,500k and 6,000k. Any less would be more blueish (cool white) and any more would have a yellow tint. Next for a reading light you want the brightness. You want nothing less than 250 lumens and more is better. 400 to 500 lumens would probably be best for a reading light. Dome lights are fine in the 200-300 range, nothing less than 200 lumens.
So, if you want to experiment with LED's that may give you a start. Just go on Ebay and search for BA15S LED lamps and pick one you think will work for your use. Lots of styles and pick a number for the amount of LED on the lamp. More LEDs does not necessarily equate to a brighter lamp. Many of the sites don't give you the lumens number but perhaps you can contact the seller and find out.
I'll pass on a little more information for anyone wanting to replace LEDs in their RV. There are several styles of base used. Some are a simple push in flat base with two wires wrapped around it, that would be a 'wedge base' or 'T10'. For a lamp with a bayonet base they can be either a BA15D (15mm diameter - dual contact) which would have horizontal opposing pins on the side or could be a BAY15D (15mm diameter - dual contacts) with offset pins on the side. Just remember, BA - horizontal pins, BAY - offset pins. Do not put a BA15S bulb in a BA15D socket unless you have extra fuses to waste. The wedge, BA15 and BAY15 are probably most common. Some sellers will provide a jumper with different base connections so if you aren't sure of what style you have you can still use it. There are some with a base made like the old style fuses used that have a contact on each end and just push in. If you want to replace exterior marker lights the T10 base is most common. Just make sure they are not too long or they will not fit under the lens cover. An LED that is 28mm (1.1 inches) long or less will work. A 28mm long LED will most likely be 5 LEDs and it will just barely fit. The lamp will be right against the cover but it will work.
I buy most of my LEDs on Ebay. Some come from US distributors and many from China. Lets be honest, they are all made in China. Shop around because prices will vary all over the place for the same LED.
I replaced all the lamps in my little old RV, inside and out and you get a little smarter with each lens you take off. Most of the interior lamps were 200 lumens and the brake/turn/tail light was dual intensity and had a max of 500 lumens. Some RVs will have separate tail and brake/turn lamps.
Good luck in finding the lamp you need.
2014 Palomino Puma 25RS
2011 F-150 Super Crew XLT
Days camped in 2014 - 23
Camped 2015 - 47
Camped 2016 - 51 done - 6 more planned so far