The new design for the corner cap uses a pair of technic bricks at each end of the cap. The pair consists of an axle brick and a pin brick. On the left edge (when facing the modular baseplate) the bricks face out, with a 3x axle w/flat head inserted as shown.
The corner cap is on a 2 x 10 plate.
NOTE: You could also use the 3 x technic axle with the bump on the end, simply sandwich the axle between the two bricks.
The straight cap is the same design, but on a 2 x 8 plate.
For each modular baseplate, one straight cap and one corner cap is required.
Module caps would attach to a 2 unit base system as follows:
Using a single axle brick in each joint pair reduces the tension required to detach the caps from the bases, while adding stability to a completed unit.
You can also attach an edge cap and corner cap to each base, then attach two base units together with caps already attached.