It will be safer to consider removing the mirror from the assembly to make sure it doesn't break accidentally. To remove just the mirror, just start clipping it away from the bottom and it will come out easily.
1. Now, on the underside of the ORVM assembly, there is a flap acting as a cover and a gasket which is held by one small 4-head screw. Unscrew it to remove the flap cover.
2. Once that flap is removed, it will reveal 3 more 4-head bolts which need to be removed to open the assembly further. 2 of these 3 bolts in my case were rusted and refused to give up. I used Zorrik but it still didn't help loosen them. When the heads of the bolts gave up, there was no option left other than widening the hole and removing the shoulder of the ORVM. Those stubborn bolts were removed by help of pliers later.
3. Undo 4 more screws holding the frame/ trim around the mirror and that will free the complete actuator assembly.
4. Locate the actuator and open the plastic cap held by clips.
5. Once the plastic cap is removed, you can see the actuator motor and a small electronic circuit. As you would imagine, this is the motor which helps open/ retract the ORVM. The function of this small electronic circuit is special. This cuts off power supply to the motor once it senses a resistance in the mechanism. This is why if the mechanicals inside the assemble break down, the motor would continue to run infinitely because there is not enough mechanical resistance in the assembly. We need to remove this circuit. It has 2 pins hooked to the motor. Sliding the circuit out will do the job.
6. Under the circuit, there are 2 screws waiting to be undone. Remove them and pull the sub-assembly out. This now reveals the mechanical gear arrangement. In the Civic, there are a total of 5 gears- one non-removable mounted on the hinge. One plastic spiral gear is mounted on the motor spindle and connects directly to a plastic helical cog gear. This helical cog gear is directly plugged on a metal worm gear which connects to another metal cog. All except 2 gears are made of plastic and most of the time, the larger plastic helical cog gear is the one which split-breaks and results in gear slippage and hence the issue. I found the same in my case.
7. Remove all gears and wipe clean the broken gear. As the entire internal mechanical arrangement is smeared with lithium grease; one needs to clean the gear thoroughly which needs to be pasted. If you can arrange a new part, so much better and convenient. But I am not sure if Honda or any ASC sells this as a child part. Most of the ASCs sell the entire actuator electro-mechanical assembly at the minimum. Some after market supplies from sites like Ali Express or e-Bay may save the day for you.
8. Since I didn't have the spare, I decided to glue the gear; but unfortunately just gluing the gear didn't help. If going for a paste-job; use a strong adhesive. I used Araldite. I not only glued the gear itself but to ensure proper mechanical strength, I had to glue the gear on the worm gear too. This would reduce the stress on the cracked gear, and it actually worked that way. Before gluing, I gave the gears a proper WD40/Zorrik bath followed by a soap solution wash to remove any traces of oil and grease that would affect the strength of gluing outcome. Also, I sanded the areas to be stuck to make the surfaces a little rough.
9. Since the epoxy/resin takes a considerably longer time to cure; I left the gears to dry out for a couple of days. Before the epoxy dries out completely, care to remove any excess glue to make sure you don't alter the gearing resistance accidentally by leaving glues between the teeth.
So, after the epoxy resin cures completely, re-assemble the mechanism in reverse order. If you can bench-test the assembly- good; if not, just reattach the ORVM to your car and plug into the wiring harness and test it.
I would have ideally wanted to replace this cracked plastic gear but because of non-availability of this part made me go this way. I hope it holds on well. Right now, it is working perfectly since a week a now.
Trust that will be of help to someone in need.
Thanks.