Silverstrings, I'm glad I could be of help.  I and everyone else on this forum was once at the same place you are at in learning the dulcimer.

Continue to ask questions when you feel the need.  Someone on this forum is ready and willing to help you discover the answers.  This forum is home to a great bunch of people.  They freely share what they have learned during their own journey with the mountain dulcimer.

Thanks for all the great insight and advice. I realized once I got to my Dulcimer Group, that my technique was the problem.  Greg Gunner, I think you nailed it. I am new at this so I am actually glad it was not my instrument. I even tried my bad technique on my Teacher’s standard McSpadden and realized I did the same thing! I appreciate all of you at FOTMD! Great site.

26" is shorter than most standard McSpaddens.  You are also tuning CGC- lower than the most common standard tunings. The combination of these two factors means your strings are a little bit looser than normal setups.  Looser strings means when you pluck them (or pull offs), the arc at which they vibrate will be wider... they'll move more when vibrating.  This makes them accidentally buzz against one or more frets.

You can make those strings a bit more taut by one of two ways:  either tune UP a step to DAd and play in the key of D, OR simply get some slightly thicker gauge strings and put those on.  Thicker strings will be tighter even if you stay in CGC.  Look for strings that are just one step thicker-  for example if the current string is .022 get .024 instead.  
That's probably all you need to do for the buzzing to be gone. Fresh strings that are a wee bit heavier... thus tighter with less wild vibration arc when plucked.

When plucked, the string will vibrate to produce sound.  I'm certainly no expert, but I suspect the buzzing is related to two factors: 1.) the direction in which you are plucking the string and  2.) the space between the string and nearby frets.

If the plucking finger is pulled off "parallel" to the fingerboard you will have less buzzing because the string vibrates from side to side making it less likely to contact nearby frets.  If the plucking finger is pulled up in a "perpendicular"  direction from the fretboard you may have more buzzing because the string vibrates up and down making it more likely to make contact with nearby frets.

Obviously the space between the string and nearby frets will also play a part.  The string is closest to the frets at the peghead end of the fretboard.  This may explain why you are experiencing the buzzing only at the 1st and 2nd fret.

Since the string only buzzes when you do pull-offs I suspect it is related to number 1 above, but it may be related to how forcefully you pluck the string.

I get buzzes which seem to be weather-related.  Just a thought.  Though the wood is no longer living as a tree, it 'lives' in a different way now, subject to all sorts of changes. 

Without actually watching you, I suspect it's your technique at fault, not the dulcimer.  Especially since it's not an every-time thing. 

Your cheap guitar doesn't do it because,  1. You've been playing guitar longer; and 2.  The mechanics/physical movements of a pull off with your hand wrapped around a neck vs. your hand on top of the fretboard are two completely different things.  Apples and oranges.

VSL and tuning shouldn't matter one iota, unless your strings are a very wide mis-match for the tuning. and the strings are very floppy.

When I am practicing pulls offs on the Bass and Middle strings on the 1st and @nd frets, sometimes I get a buzz and sometimes not. Seems like I have to pull off very lightly. Is this due to my technique or lack of technique? I just got a wonderful sounding McSpadden so I hope it is me and not the instrument. My cheapest guitar doesn’t do it when I pull off. 

Any suggestions? Thanks

FYI, it is a 26”vsl and I do tune mostly in CGC because my Dulcimer tunes to CGC.