Clicking noise coming from under the glove box while starting

Blower Motor

that item is called a relay switch. it toggles on and off depending on which electrical component it is connecting. if it's blown, they are cheap and easy to replace like a fuse, but you'll need to look at the fuse box chart (usually on the underside of the lid) to determine which one and where it's located. You can't look inside the relay to determine if blown, but you can replace them one at a time to test...
Also, if you're experienced in electrical, a paper clip can be used when the relay is out, to connect the circuit that you need. use tools and or gloves when attempting this method.

The noise is likely the AC/Heater temperature control blend door moving. Some noise is normal

Agreed the recirc actuator is bad.

relay clicking?

it sounds like your starter relay is working (thats the clicking you hear) so the problem possibly lies withe starter motor or the solenoid mounted on top of it.

the location and type of noise u hear is most likely coming from the electric blend door temperature control actuator.when they fail the ting gears inside make a clicking noise like this, the location you gave is dead on to where this part is located.

It may be a relay clicking. You can test the relay with an ohmmeter or multi-tester. Have you noticed any components not working?

You have an ECM and a BCM, one located behind your glove box and the other underneath your passenger side dash. They are very similar in size, shape, and color but i think the ECM s behind the glove box. I had the same problem and replaced the one behind the glove box and the problem went away. They are both easy to replace but they cost around $70 if I remember correctly. And you have a chip you have to swap from the old to the new that you have to be careful with.

just under the pressure of the car or tune it up its normal for civic