Fretboard separation from soundboard...
From the photo, it looks like the spruce top (?) has broken away from the fret board and some spruce is still attached to the fret board. (A good glue joint is stronger than the wood, so that may be the case.) If that's so, (and it looks like the joint between the head stock and fingerboard is firm) then the wood may have shrunk and separated. At any rate, consider fixing/filling the gap with a liberally glued and snug fitting shim. That would secure the two parts again.
Hello CD, if the fingerboard pulled away from the soundboard then clamp as Ken said. If the soundboard pulled away from the fingerboard, then clamping would warp the fingerboard. If its the latter then add a shim between them. Its a common problem with all dulcimers over time where the soundboard pulls away a little bit from the fingerboard, usually on one side. If your dulcimer plays well as is, then you might want to leave well enough alone. Wood is very fluid over time its all a part of getting old I guess... Robert.
Slack the strings.
Use a large C clamp and padding right where the fretboard ends, and see if you can GENTLY squeeze the gap shut, even just a little. If so, that's better/good. Use thick, slo-setting superglue and clamp for a couple minutes until things set. Otherwise you'll have to fill the gap.
Use painter's tape to mask the sides and under the arch, and use thick superglue to fill the gap. This may take several applications.