Related? https://www.t3x.org/files/floodfill.pdf

Basic interpreter for the code:

https://www.t3x.org/nmhbasic/index.html

To compile it:

       unzip nmhbas3_32.zip
       cc  -O2 -DEXTRA -o tcvm tcvm.c
       ./tcvm basic 

To run some basic programs:

      ./tcvm basic maze.bas
     #3 = maze.bas
     load #3
       OK
     run

Exit to your OS:

     system

OK, let's run the floodfill example from the PDF:

      ./tcvm basic flood.bas
      #3 = flood.bas
      load #3
       ok
       run

For a puzzle of this sort I would expect to be able to create multiple path segments and connect them later. I would be able to do this with paper and pencil. For instance on the first puzzle you can deduce the way 2 and 3 must be connected without knowing how to connect 1 and 2.

I came to say the same thing. If you have to reach every cell, then you can immediately draw in the corners, for instance.