congrats on the jeep, and for your first post.
1) you've got a good vehicle there, price was perfect.
2) you're going to spend a few bucks on oil, filter, fuel filter, air filter, zerk all the grease fittings, and maybe plugs/wires/cap/rotor if you are further inclined.
3) these are good vehicles and tend to have a very long life. abused ones last quite a long time, too, they are very solid and dependable and even better if treated right
4) ok, enough of that, now you have to deal with the brake problem:
first, check brake fluid. (of course)
next, check master cylinder for leaks
you most likely have a bad master cylinder that still works, but there is a worn seal of the several, and the left/right braking balanced action of the fluid piston is overtraveling either front or rear, and this is what is triggering your brake light. it is the first indication that your (proabably) master cylinder is going belly up. if the brakes are mushy, or it pulls to one side, you may have air in the lines which can be bled out.... BUT...before you bleed brakes, place a 2x4 under the brake pedal and DO NOT PRESS THE BRAKE PEDAL TO THE FLOOR WHEN YOU BLEED OLD BRAKING SYSTEMS....(i'd say more than 50k miles) because all the crap at the end of the master cyllinder will be shoved into the o-ring seals, cut them, and then 2 weeks after bleeding the system and everything being ok, you will suddenly experience brake pedal going to floor when stopping....YIKES....so take it from an experienced wrench.
anyhow, you have several choices, here's what i'd do:
1) bleed brake system with above suggestions
2) if light still stays on, take it to good brake place for a freebie estimate
3) most likely, you have a bad/internal problem on your master cylinder
4) do it yourself, buy a new (not rebuilt) master cylinder, or at least go to NAPA. stay away from pep or trak lifetime warranty ones, you'll get good at swapping those out from time to time...yes they work, but go for quality (like tires) and don't go cheap on brake components.
5) have shop do it otherwise, and prepare to pay $200-300
let us know how it goes!
Newly Painted! Emerald Green '96 XJ 4x4 4.0 HO 5-spd
3" Lift + 31" Tires / D35 TracLok / NP231
Drilled out Stock Airbox / Gauge Cluster Upgrade
Magnaflow Muffler / High-flo Cat / MSD Coil