I have a two-line desktop phone where a red light indicates if a given
line is 'in use'. Lately, i've noticed that 10 to 15 seconds after I
hangup from a phone call that line's light will blink back on for less
than a second.

One line is my conventional land line - the other is a Vonage line.
Both lines act the same way. The phone itself is relatively
inexpensive 2-line conventional handset/speaker/plug for headset
model...not a PBX or other digital featureset. AT&T branded model 982.

No, it's not being bugged.