I have been thinking of this very project and I have two 5M rolls of 5050 LEDs but now I am thinking of running in rain and with the oil residue coming up from wet pavement etc that the adhesive is going to let go sooner or later and you will have a hanging wire situation. As well cold weather may release the adhesive.
Thusly I am now rethinking the various application modes and more along the lines of LED Modules that can be attached to the belly pan with self tapping No 8 hex drive metal screws. The modules seem to be waterproof but make sure before you order and they come in colors and if you don't want to run through wheel wells just splice in jumper wire in the circuit.
There there is the question of whether you want them on while running wired through your tail light circuit or just want to have the ability to use them in camp grounds and exterior lighting.
I am going to wire in a Astron 7 amp power supply and run circuits out from it. Figure I will put it in behind microwave and plug it into that recepticle so when shore line is hooked up the second circuit is up and running automatically. The Astrons are used by Ham Radio operators (de AC4HT) and are controlled right on 13.8 volts for a solid steady power delivery which gives long life. If I remember my calculations right a 7 amp Astron should power up to 33 watts of LEDs and that is a lot of lights. They also come in 10, 12, 15 and 20 amps but of course they are bigger/heavier.
Note: you will see smaller power supplies advertised for these but for the cost of two or three of these good for one circuit you can get a Astron for same price and run perhaps 16 circuits. You can pick up Astron 7 amps on ebay for 20.00 to 50.00 used (which is what I did). A Ham had added two 4 terminal junction blocks to top of unit thusly I can run 8 circuits at one time. If anyone wants to see how he did this PM me and I will email you a picture of how he did it.
I just got a 500 ft roll of 18/2 AWG shielded and color coded red/black for this second wiring program and will control all of them with shallow rough boxes and 120V commercial light switches next to our twin beds that are right over the wheel wells giving easy access to outside without drilling. I got it on clearance at Lowes and got about $15.00 off on it. I also have a partial spool of 22/4 AWG (flea market find) I could run soldered to end of 18AWG outside thus one hot line becomes 2. These will not be grounded on AS but return to Astron to make the circuit.
The modules come in white, red, green and blue depending on your desires. Below is a good pic of how they come and shows the mounting holes for attaching them to surfaces. They have adhesive on the backs for the initial placement but as indicated I don't think it would last long haul with road film,vibration etc. Least ways with the screws you could apply a drop of Loctite 222 to screw threads which should eliminate the vibration loosening problem.
40pcs SMD5630 White 6000K 3 LEDs Module Waterproof DC12V High Lumens | eBay
5630 LEDs give the most light,then 5050 slighly less and then there is the 3000 range lights that are much less. Thus if you do a search add in either of those numbers and make sure they say they are waterproof because I have come across some LEDs that are not waterproof. Also the white or bright white are just that but the WARM WHITE gives the appearance of a standard incandescent bulb light.
I thought as a first circuit I would put in a line down the curb side looking outboard to give ground light for walking around outside at night.
Note: All the LEDs I have run up on yet are wired with 23AWG thusly 22AWG or heavier should take care of anything you need I would think.
Also to be considered if you run them in blue, red or green they don't destroy your night vision. Thusly I have blue LEDs in truck cab overhead so they can be turned on and still see to drive.