General mountain dulcimer or music discussions
I'm no expert on autism, but if you think math might be the key to getting your granddaughter interested in music, there are lots of places to find it.
Right hand strumming is all a matter of fractions. Does your daughter already know about note duration? If we start with a tune in 4/4 time, then a whole note gets one strum to last the whole measure, but we can cut that in half and get half notes, so you strum twice in that measure, we can cut each half note in half and get quarter notes and strum four times in a measure, we can cut those quarter notes in half and get eighth notes, in which case we strum eight times in a measure, and so forth. And we can mix and match those strums, with the understanding that all those fractions have to add up to 1 for each measure.
The left hand is all about math, too, but at least on the dulcimer we don't work with fractions but integers. If your granddaughter is going to be playing other instruments--likely if her elective is band--then I would stress not the numbers of the frets but the intervals between notes. So the root or tonic is the 1st, the next note of the scale is the 2nd, the next note is the 3rd, and so forth until you get to the octave, the 8th note.
I would have her start by playing in a drone style (she can use her fingers rather than a noter, I would think) and show her a simple melody, noting the intervals involved. You might even make a game of it, playing the first notes of a song and asking her to figure out what the interval is. Twinkle Twinkle begins with a 5th. Here Comes the Bride begins with a fourth. My Bonnie Lies Over the Ocean begins with a 6th. Show her those intervals on the fretboard and see if that piques her interest.
Having said all that, you might also just put the dulcimer on her lap, show her a simple melody, and see what she does on her own. Some children with autism have the ability to very quickly learn pretty complicated pieces of music, and it might be that the mathematical patterns of music are more easily understood by people with autism than they are by the rest of us supposedly "normal" people. I think if you are attentive to your granddaughter, you might find she takes quickly to music without you having to point out the math behind it.