I've got a question on movement between the corner of the board and a block.

C is the corner off the map, B is the block and L stands for legal spaces.

C L

L B

The line of sight diagram on page 10 of the rule book with Silhouette, shows that you can trace line of site through such a gap. Can you also move through that gap? We had been playing that you couldn't since it was adjacent to the corner, but the example shows that line of sight can be made. Thanks in advance for any advice.

Look one page back, there's also a "Movement Example" on page 9, which shows diagonal movement.

In Addition:

JitD p. 4
#Every space that is touching a given space (even at the corners) is adjacent to that given space.

JitD p. 9
#Figures may move into any adjacent space (including diagonal spaces) for 1 movement point each

So yes, you can move through such a gap (and of course trace LoS).