Present action in past tense

The context tells the time.

we usually say thank you or sorry just after completion of an action.

Thank you for watching my you tube channel

since somebody has already watched the channel,you can say the above sentence.

I am sorry for taking your pen

You say sorry after taking the pen. so the time of the action is completed in the present( present perfect)

Both the sentences may be used in oral communication since the time of the action is implied and completed in the present moment.

I think watching and taking are present participles or simply ingforms.

Without the context we can not tell the time forwhich the sentences are used.

From the point of view of my native language, "watching" in this sentence plays a role of a noun. To be more specific, it's a name of the activity. In that sense it's not a verb at all, thus it isn't placed in time on it's own.