I'd encourage you to look at an A-type OD for your car. It's a relatively simple installation, as compared to a J-type or other options. And, a "correct" OD will add to the car's value, while an "incorrect" one might detract.
Yes, with an A-type you still need to change the main shaft in the gearbox, remove the tail piece and put on an adapater plate. The top of the gearbox will need to be drilled and tapped for the switches. A different speedometer cable will be needed, too, I believe.
But, to fit up a J-type, you need to rig a rear mount, possibly have some welding done on the frame. The fit around the exhaust pipes and frame gets pretty tight, but it's possible if you don't mind the modifications.
If you only want overdrive on top gear, you only need one switch (which will actually enable it in 3rd & 4th gears). The other switch is only necessary to use it on 2nd gear.
Look closely at the gear ratios and how the A-type provides, effectively, a 7 speed gearbox. It's actually pretty well thought out and effective. I wouldn't bother with changing gears in the gearbox. I'd suggest instead to look at the differential crown wheel & pinion, if you need "longer legs" or, conversely, faster acceleration. A 3.7:1 ratio was standard in there. Many cars had an optional 4.1:1, though, and it's still available. The 4.1 does accelerate faster, but the car will be revving higher on the freeway, which can be offset by the overdrive.
Less common, but available, are 3.45:1 and 4.5:1 ratios. The first making the car pretty slow off the line, but certainly able to cruise comfortably all day at 70 mph. The latter would get you to 60 very quickly.
By the way, there were at least two versions of A-type. One has a larger accumulator piston and bangs into action faster. The A-type generally provides 22% reduction. The J-type provides 25% reduction, in the TR version. It's possible to tell by looking at the brass plate riveted on the "top" side of the OD. The first two digits of the model number indicate the amount of reduction, such as 22xxx or 25xxxx. Of course, this assumes someone hasn't rebuilt it to a different configuration during its lifetime. It's possible to do so. As much as 28% reduction is possible.
There were also non-TR A-type ODs. These often do not have a rear mount in the same configuration needed by TRs. And, the "vertical" actuating solenoid was unique to the TR version of the A-type. Non-TR A-type ODs have a horizontally mounted solenoid.
With stock installation, there really isn't that much electrical involved in an overdrive. You have the operating switch in the cockpit, one or two inhibitor switches (which are the same as the backup light swithches used on later TRs), a relay (again, a common Lucas item used elsewhere) and the actuating solenoid. The latter is the most vulnerable, to debris thrown up under the car, or to incorrect adjustment.
There are some aftermarket items that add a little complexity, such as the "black box" overdrive controller offered by Revington TR, a neat item that makes the OD operate more like a 7 speed gearbox. And, the momentary switch to actuate my TR4's OD is mounted in the car's shift knob, as a push button instead of the stock lever on the steering column. That also means a little added wiring.
If the OD is being used with a normal to mildly perfomance boosted motor, is maintained and adjusted properly, and is used in a normal manner, it should last a long time and give little trouble.
If you do decide to install an overdrive, I'd encourage you to consider having the gearbox gone through thoroughly at the same time. Since the gearbox and the OD share oil, one can contaminate the other. If the gearbox has a lot of filings in it from worn parts, they will get into the OD and likely do some damage. Vice versa, the OD should be clean and fresh before being bolted up to a rebuilt gearbox.
Cheers!
Alan