Actually that headstock break looks pretty clean. Would be a fairly easy fix. Not as horrible as it appears.
The repair would not be that difficult, and could be made to look relatively good, because the dark existing finish can be easier to match up than clearer finishes. There is a lot of wood surface for the glue to adhere to, there is no end grain involved, and there doesn't appear to be any missing wood from the pictures provided. If done properly and in the correct sequence, there is no reason that this wouldn't be a stable repair. Push comes to shove, a thin mahogany veneer could be added to the back of the head stock, and then finished to match the rest of the neck.
To be honest, I am far more concerned with neck angle and the wear marks on the sound board. Neck angle, without strings and saddle is of course, impossible to assess.The wear marks, in the absence of close up pictures, is likewise impossible to assess in terms of determining depth, and how much contamination (as in skin oils and dust adhering to the skin oils, if they are present) are present (this would affect the ability to finish the guitar properly, not impossible to address, just labour intensive). Pickguard is likewise, a minor concern. The tuners may need replacing, it will need new bridge pins, and probably a new nut and saddle.
This is a project that can work out well, but its success or failure will be dependent on the neck angle issue. If the neck angle is good, then the guitar is a definite yes going forward. If the neck angle is bad, now you have to assess whether in addition to the other repairs suggested above, the cost of the repairs plus the neck reset makes the guitar viable vs. just finding another G-312 with fewer issues.
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