I beg to differ …
My mic socket is stereo, but you could feed the stereo earbuds into a mono mic socket via a stereo to mono adapter as has been suggested.
I’d suggest increasing the sample rate on Audacity for better accuracy in the timing.
With earbuds 50cm apart the interval is 1.5 milliseconds, on the default sample rate of 44100Hz that’s 66 samples
you can only judge to within 1 sample, 1/66 is 1.5% accuracy. If you increase the sample rate you can improve on that.
Maybe metal spoons could be used as a substitute clapperboard … Spoon (musical instrument) - Wikipedia technique #1
UPDATE … spoons as clapperboard, earbuds 50cm apart …
So having tried it using earbuds as stereo mics, a mono mic won’t work : the second (weaker) signal from the furthest mic will be lost in noise.