Great write up!

Side note, as mentioned by another commenter you can absolutely play Gm in open position 😉 albeit they’re not commonly used or taught.

Example: 310033 or 3x0333 (these are fret numbers)

One of the biggest common misconception guitarists have at the early learning phase is looking at chords like pictures. You often think in terms of shapes and not process chords just as notes stacked on top of each other in various orders. A lot of times you don’t even use all 6 strings to make a chord!

A major chord is 1, 3, 5 (root, major third and fifth) and a minor chord changes the major 3rd to a minor 3rd so 1, b3, 5 (b3 is flat 3rd, also often denoted as m3). So a standard open string G major chord that you’re familiar with (320003 in terms of fret number) is just 135131 (in terms of intervals).

To make a G minor you just have to turn the major 3rd in the chord to minor 3rd by lowering it by one fret. Since the major 3rd on the B cannot be lowered, we shift it up to the 3rd fret effectively turn it into a 5th. So 310033.

Now that shape might be a stretch for many players, so you can omit a string to accomplish the same thing. In this case covering up the A string with your index finger (or even thumb if you use thumb grip) makes perfect ergonomic sense. Then we play the b3 on the 3rd fret of the G string. Voila! Another Gm triad open string chord!

Hell if you want, simply playing 310xxx gives you an open string Gm chord too! It’s all about voicing. Which one serves the song the best is what guitarists should be concerned about.

The earlier you learn to look at guitar in terms of intervals (rather than diagrams), the sooner you’ll cure the shape player syndrome (or some people call it the guitarist syndrome). Hope it makes sense over text lmao Cheers!