I can't stop sending positions remotely by explore.garmin.com

I'm not sure why you'd want to do this if the device is in your possession. Note that stopping tracking this way does require the device to be powered up and have a clear sky view. If the unit is successfully sending points, then that condition is met. 

If I had to GUESS, I would GUESS that the servers are not sending the stop request in a timely manner. But it's all speculation. Open a support ticket.

In this case, the device is not in my possession. I want to activate and deactivate that sending remotely, via web (explore.garmin.com). Turning it on works, turning it off doesn't (at least in my tests)

I have opened a support ticket. Thank you :)

I answer myself (although in reality your answer was largely correct, @twolpert, thanks): I'm wrong because remote deactivation of sending points via explore.garmin.com does work ok, but it requires patience and sometimes takes up to 1 hour to do it.

I have been doing more tests and what happened is that if the device is not sending or receiving anything, it can take up to 1h to synchronize with the Iridium network to send/receive messages or instructions (like this "stop tracking" instruction).

Thanks to the Garmin spanish support service that has given me the correct clue: wait more.

On the other hand, I see that, in addition to correctly disabling point sending, it also disables local logging in the tracking's inReach. Turn both things off. I would like to turn off just sending points, but the person I do that to remotely also has local logging turned off, so they don't have the option to do a trackback, for example.

Logically the person can do everything locally (activate/deactivate what they want: sending and/or tracking, but I'm talking about doing it remotely).

The fact is that it works for me as it is, so great.

By the way, activation costs 2 points and deactivation 2 points (0.40 euros here). It's a good system.

The "up to one hour wait" suggests that the device does not "see" the change until it does a message check. By default, iR devices check once an hour. The device will also do an implicit check any time it sends something (message, track point, or whatever).

That would suggest that (with tracking on), disabling tracking should occur after the next point is sent. Not sure if you are seeing this behavior or not.

Enabling tracking (with tracking off) won't occur until the next automatic message check, which might take up to an hour. Or until the person who has the device sends something.