Not on my Typhoon H. I also checked an H Plus.
If the rear LED is flashing red, it suggests you have the Mode switch and the Landing Gear switch reversed, or you are operating the wrong switch. (Or, I might be about to learn something new.)
Note Hardware Monitor is not fully revealing on the TH. You should check the "final output" graph. Do a fast double tap on the Volts display of your ST16. A chart will appear showing 24 channels. Operating the Landing Gear switch should show a full scale change on Channel 11. Operating the Mode switch should show changes on Channels 5 and 6.
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It may also be helpful to upload a screenshot of your firmware page, such as this:
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