Based on my previous exposure to this type of repair system and confirmed for your convenience in a YouTube video, the hot staple gun is aimed at repairing and strengthening flat surfaces of some thickness. If the stalk has snapped close to the column, you may not be able to get the tool in a suitable position for securing the insert. Additionally, it would be optimum to secure at least four inserts spaced around the perimeter of the stalk.
A photo would be useful to better identify the problem area but an image search using terms "1988 honda accord turn signal stalk" presents a reasonable collection of images of the mechanism. One such image is of an expired eBay posting, which means this image is attributed to the search, not to the original creator:
As I believe this tool isn't particular well suited, consider to sleeve the stalk. This would require a reasonably substantial length of open area on both sides of the split. It should be a minimum of 1.5 times the diameter, but aeronautical engineering specifications don't necessarily apply here. An aluminum tube of correct inside diameter placed over the pieces, liberally slathered with epoxy would provide increased strength in comparison to simple surface adhesive.
If possible consider also to internally sleeve the stalk. Use a smaller diameter tube (obviously) and cut a slit if needed to pass wiring through. Using the same 1.5 times diameter reference, the length provides support. Using both inside and outside sleeves will give you best results.