Why does my new 67i make random beeps while I'm hiking?

Are you navigating a course or route? If so then it could be the unit making a sound to signal you're nearing a turn or waypoint (depending on settings and navigation option used).

If you don't like the beeps you can change or disable them in Menu > Setup > Tones.

Thanks.  I'm not navigating, I'm just recording a track, with tracking off.

Hmm not sure what it is then... Do you have the device on key lock when using it? Perhaps unintentional button presses when in a pack or something like that?

And is there any message at all on the screen when the tone sounds?

I carry it on my shoulder strap, so nothing is pressing the buttons while I hike.  And no messages appear on the screen.

Have you tried a reset yet. Turn the unit off , then press page and enter simultaneously and hold them down while you power up the unit? You will have to set it all up again, but it could fix it. Also as mentioned above you can turn off all of the tones, proximity, inreach, message, key beeps, and turn warnings. Perhaps you can do some troubleshooting, by turning off one or two at a time to try to find out what’s going on. A little time consuming, but it might help you figure it out.

Final thing then I can think of: do you walk through areas where signal reception is bad? The GPSMAP 67i will beep when it has lost the satellite signal. It will also show a message but when satellite reception is restored the message disappears.

If this is the case check that you have multi-gnss and multi-band are configured correctly (Menu > Setup > System > Satellite).

I think you've nailed it.  I was hiking under heavy tree canopy in a valley in the Pacific Northwest, and I'm sure it was losing reception at times.  I previously had an inReach Mini, which didn't beep when it lost reception.  And the Mini often had poor reception.  One of the reasons I bought the 67i is that I had the impression that its reception would be better, because it has a more elaborate antenna.

Glad we were able to figure it out

Be sure to check your satellite settings then. If you use Multi-GNSS and Multi-band the 67i has more satellite systems (and signals) to choose from so the reception may be better. You can check your settings under Menu > Setup > System > Satellite.

And you can always use  the Satellite page to see from which satellites the 67i is getting its signal.

Yes, I hadn't enabled multi-GNSS, which probably explains why I was losing reception.  Do you know whether multi-GNSS cuts into battery life?

Perhaps this is a little bit helpful:

www.garmin.com/.../