As a teenager I used to have a summer job on a cattle ranch in that area, near Durango/Silverton. Surely is God’s country. I thought I was going to ride horses as part of the job but it turned out I was assigned to drive a 1967 VW Beetle around on the ranch’s rough, rut-filled dirt roads and run errands for the cows. That was fun too. But I wished I could have ridden some horses too. … …anyway so one idea would be to trade in the LR and buy a 1967 VW Beetle as that car never failed me once … lol
Back to being serious … The CEL problem, that’s one thing you’ve learned, when buying a car, to make sure all the dash lights come on that should when the key in in “on” but the engine is not started. On my Corolla the CEL, battery, brake, seat belt, and oil pressure warning lights all come on. The car will still work with the CEL bulb not working, but the CEL system is the most effective method for how mechanics figure out what is wrong these days. Cars are just too complicated otherwise, too many interactions, too much of a guessing game.
I don’t see how brake work could have caused this problem, but anything is possible once the car gets into the shop and people start working on it I suppose. A connector could have gotten knocked loose maybe. When I read your post my two thoughts were something wrong with the evap system, or with a crank or cam sensor. Usually those would throw DT codes of one sort or another. Do you know if you have any active or pending codes present? One thing you could try as an experiment, next time it happens, try temporarily loosening the gas cap and see if that helps. Don’t drive that way of course as it is unsafe.
If all else fails you may need to take your LR to a qualified LR service center. A dealer or inde that specializes in LR’s. Where’s the closest? Grand Junction, Albuquerque, or Denver I guess. Best of luck. And don’t forget that idea about the 1967 VW Beetle!