I figured I'd make a post about how I learned the fretboard in case anyone was interested. It's a lot easier than you think -- but still work. I'm not going to get into the benefits of knowing the fretboard, to each their own. Aside from just brute-forcing, I found I relied on two methods that made it a lot easier and reinforced each other, one involves learning a scale throughout the fret, the other involves learning the notes in the chords of a G Major scale. One technique that helps A LOT is that you can practice without the banjo in hand. Before you go to sleep, on your commute, whatever, you can visualize the fretboard and start running through the following exercises. I promise it helps. The next time you pick up your banjo things will work more fluidly.
G-A-B-D-E-G
The goal is to play no more than two notes on a single string. We're going to start on E and as we move down the fret, we’ll always start on the 4th string.
E G A B D E
|----------------2-|
|-------------3----|
|-------2--4-------|
|-2--5-------------|
|------------------|
Say the letter, hear the note, sing it. This is important because you want to start internalizing the sounds.
Then move on to the next letter in the scale, G.
G A B D E G
|----------------5-|
|-------------5----|
|-------4--7-------|
|-5--7-------------|
|------------------|
And so on until you run out of fretboard space. Afterward, you can begin experimenting with replacing notes with their open counterparts. The following is equivalent to the measure directly above. You should figure out open note alternatives, or variations of the scales all the way up the fret.
G A B D E G
|----------0-------|
|-------0-----5----|
|-0----------------|
|----7-------------|
|----------------0-|
It's important for you to figure out the scale at different positions yourself, struggle! It will help you remember. And you'll begin picking up patterns and saying to yourself, I need an E here, I know I have an E there, is there a more convenient place I can hit it?
The first step is to learn the notes in the chords in the G Major Scale. Just brute force this, use flashcards/pneumonics. The G Major Scale is composed of G A B C D E F# -- this is your alphabet, all the chords you learn will be composed of these notes.
Am - ACE Bm - BDF# C - CEG D - DF#A Em - EGB F#dm- F#AC G - GBD
There are three main shapes that you should already know, the F-shape (root position), D-shape (1st inversion), and Bar (2nd inversion). The names in parentheticals are a better name for those shapes, so we'll use them. Those describe the chord's voicing -- voicing is the idea that a chord can be arranged in multiple ways like the following example of a G-major chord:
Root 1st 2nd
|-5(G)---9(B)---0(D)-|
|-3(D)---8(G)---0(B)-|
|-4(B)---7(D)---0(G)-|
|-5(G)---9(B)---0(D)-|
|--------------------|
There are a lot of incredibly practical patterns going on above. The first is that when you make a root-position chord, the fourth (and 1st) string will always be the same note as the chord you're making. If you're in 1st inversion, it will be the second string. For 2nd inversion, it will the third string. Fret the chord, say what inversion you're in, play each note, say what they are -- sing them. Do this for every chord in the G-major scale as far as you can on the fretboard.
As an aside, one neat trick thing is that if you remove the lowest note in each chord, you then move one inversion. Remove the 4th string from root position G, and you now have a 1st-inversion chord. Likewise, if you remove the 4th string on the 9th fret from the 1st-inversion chord, you have a 2nd-inversion chord. Remove the low D from the bar chord and you have a root position G.
Aaaaaand that's it... Good luck all, hope this was helpful!
*Edit: I changed the first scale so that there are no open notes and it continues with the next scale.