Using real life field repair facilities as a baseline. It's easy to imagine scenarios in which players must manage resources (time, spare parts, personnel, etc.) effectively in order to maximize the combat capability of the battle damaged machines under their care. Of course there could be all sorts of cool science fiction gadgets to play with like gyro alignment setters, fusion diagnostic scanners, laser synchronization optics, and joint actuation calibrators. In addition to this, more mundane tools could be tossed into the mix such as armor cutting torches, fire suppression equipment, and liquid refueling systems.
On the management side of things, salvage costs offer up an interesting dichotomy that would add some depth to the gameplay. Do you cannibalize one machine to get enough spare parts for two more? Is it worth sending out a recovery team to pick a distant elite model wreck when there are several closer ordinary designs that could be recovered in the same amount of time? Do you spend some extra effort on preventative maintenance, or do you save a bit but risk mechanical breakdowns?
It sounds kind of crazy that anyone would want to play such a game, but I think there is a niche audience for it. If you look to at the old table-top RPG Mechwarrior, the first edition only allowed players to take the roll of mech pilots because designers thought, "Why would you want to play as anyone else?" Well...as it turns out some players actually did want to put themselves in the shoes of support personnel. So when a second edition eventually came out it made provisions for players who were interested in the archetypal roles of technician, scout, or merchant.
Obviously, we're talking a small development team, low-budget affair. Which is fine because the concept is all about popping the hood and rummaging around, not going on some graphics intensive test drive across meticulously rendered landscapes. Heck, you could even work in a progression system in the form of facility upgrades and more experienced assistants.
If Papers Please can take the rather bland sound idea of being an immigration officer and turn it into a spy thriller, I don't see why a mech tech wouldn't have at least as much potential for storytelling. Imagine, for example, having a saboteur in your midst...or more dramatic still you are the one doing the sabotage! Perhaps some rival organization is blackmailing you, maybe you have been kidnapped and are being forced to repair enemy vehicles against your better judgment. There is a lot of possible ways to get the players (in-game) hands dirty; both literally and metaphorically.