Two questions:
1. I added a 12v to 5v converter by tapping the wires to my auto dimming mirror on my 1998 Explorer XLT 4.0 SOHC. I plan to run a dash cam off the converter. That circuit is protected by a 15A fuse currently. Should I bump it up to a 20A fuse?
2. I don’t know if this was always the case, but on testing the converter installation, I realized that the compass and temperature readout on the overhead console dims when I get the car running and dim further when I switch the headlights on. Makes sense as there is more current draw in a running car. But it has me wondering - should I put in a higher output alternator instead of the stock one? Would that solve this?
Can you elaborate more of what you have done?
I just took a look at a wiring diagram and see no 15A fuse for the auto dimming mirror *
alone*, that it has on the interior fuse panel, a 7.5A fuse 11 (hot in run and start) and a 7.5A fuse 36 (hot at all times).
If you mean that there is a larger fuse handling more than just the mirror, in the engine bay distribution box, that is not where you'd want to make any changes. Instead you would calculate out how much additional current draw this dash cam uses by checking the datasheet if it is not on a sticker on the unit itself, factor in the (in-)efficiency of the 12V to 5V converter (probably around 85% assuming switchmode instead of linear regulated), to come up with a total.
Once you have that total, which is probably 1A or lower, then you can determine whether the circuit you tapped into has the margin for more current. This depends on the wire gauge to it, of all wire upstream of where you tap in. How you tap in, also determines the current limit but 1A (if in that ballpark) is pretty easy to achieve with any means you use as long as it's not wrapping bare wires together and only covering with electrical tape instead of proper wire nut if not soldered, crimped, or a distribution block.
Generally speaking, no you should not put a larger fuse in a circuit unless you know all the specifics, exactly what you're doing. More often and in this case, what you want is a separate inline fuse between where you took the tap, and this add-on circuit. Suppose it uses 1A, a bit more surge current upon power-up, then a 2A slow blow fuse in series would be reasonable.
As others mentioned, the overhead console dims with headlights on because they designed it to do this, with the assumption that you turn headlights on when it is dark out, and with it dark out, it is dark inside, so you not only do not need as much brightness to see that, but also too much brightness would interfere with your night vision more. Some degree of brightness adjustment might be available on the control wheel to the left of the steering column.
I don't know if it is accurate, but my build data (based on a vin lookup) for my '98 XLT indicates that it came with 95A alternator, and that would still be plenty for your purposes, though when it came time to replace my alternator, I did get a 130A just because I might as well.
In summary the main two things that you "probably" need to do are as mentioned above, make sure that your tap into the circuit is secure and conducting well, and put a fuse on the wire you take from that tap, near the tap as what you are adding is far more likely to have a problem later than the factory circuits, so this fuse you add will just cut off that instead of the mirror and whatever else might be on the same 15A circuit you're referring to.
I also assume you are doing a proper tap, not one of those crappy tap-fuse things where you take out the factory fuse, put the tap-thing in the fuse holder, then put the original fuse in the tap. Those put extra strain on the fuse box contacts, can wiggle themselves out, and cause poor conduction at the very least, and if that poor conduction creates heat, can start to melt the fuse box in that area. They really shouldn't exist regardless of the fact that some people have used them without issue, but there is really no need to risk any problems when you can instead do a proper tap instead by splicing into the wiring, or using an unused fuse box position, or even making a separate run to the battery.