Pick a tune you know well, and finger it with your left hand, without reaching out to get your instrument. Close your eyes and visualize where your fingers should go, then put them down and pick them up as you need to.
Can't do that? You don't know the tune. You can, however, work it out.
A D scale starts with an open D string. Think it.
Then, your first finger goes down, your second and, after that, your third. Next, pick all your fingers back off the imaginary strings and play the next open string: the A. Again first finger down, second down, then third and you're all the way through the scale to the high D.
All of this is imaginary, of course, so imagine hearing the notes, too. Hum them if it helps, but move your left-hand fingers while you're doing it. Run up and down the scale slowly a few times. I just move my fingers slightly, but touch the fingertips to your thumb or the tabletop if you want something tactile.
Do the same thing with an arpeggio -- the notes in a chord. For the D, that's open, second finger, open, third finger, to go up; then back down with open, third finger and open. D-F#-A-D-A-F#-D. You'll hear yourself in a bad cartoon of an opera singer practicing: La-la-la-la-la-la-la. Run up and down those notes a few times.
After you have that down, go back and hum a song in a key you know and play along with your left hand. Where's it start? Arkansas Traveler is a D tune, so it starts on the open D string. Yankee Doodle is in G, so it starts with the third finger on the D string -- the G.
Now what? Now pick a simple tune you've never played and work through the melody. You have to be able to hum it, but Twinkle, Twinkle Little Star, Baa-Baa Black Sheep, or a Beatles tune.
Where's it start? Chances are, it starts on D, A, or G, depending on which of those keys you want to play it in. If you stick it in the wrong key, you'll run out of notes as you go up the scale, and you'll know you need to start over in a different key. If you try one tune and can't figure it out, try a different tune.
Melodies are mostly scales and arpeggios, so when the tune's going up gradually, it's a scale, and when it jumps, it's an arpeggio. Ditto for down. If you can't tell which note it jumps to, walk up or down the scale in your mind until you find the note, then go back to where you started and make the jump.
My point here is that you can play tunes without your instrument. Even if you can't tote your mando around with you, you can play all day long in your mind, working through tunes and arrangements.
When, at last, you do open your case, your mind's already done the hard work of learning how to play the tune. Now just use the instrument to also make the sounds come out so others can hear them.
I've heard stories of professional musicians coming out of POW and concentration camps who played better when they came out than when they went in. The discipline of playing daily helped get them through the imprisonment and all the practice paid off. All this without actual instruments.
Joe Cocker wasn't just on something, he was on to something.
