Yes, two pieces of ply either side of tubes and filler ply in between. Useful to have a soild wood capping. Detail design dependent on your pushpit, but follow your picture as a guide.
Whether it is worth the aggro, or will be cheaper than a commercial one is debatable unless you have "scrap" wood to use up.
I made one last year with 6mm ply and some scraps of hardwood. Slightly more fiddly than I expected, to get it to fit nicely, but not difficult or particularly time-consuming.
Takes 3 pieces of wood. 2 are outer thinner ply facings, 3rd is inner pad piece cut to fit the rail - that is 3 pieces.
So you basically cut the inner piece (1" softwood is fine) so that you have one piece that sits along top of rail. Then two rectangles that sit either side of vertical under the top rail. You glue these to one face so that it fits rails ready to have other face bolted up to it. There is no real need to counter sink the heads / nuts in if you are careful about where they pass through and dont' foul the o/board mount.
Of course all pieces should be well soaked in suitable preserving finish of choice.
i made 1 similar from a block of Teak
i drilled 1 hole straight through & another @ 90deg forming a Tee
then cut the block in 2 to give 2 x 1/2 Tee holes
fit the 2 halves to the Stern Rail when a close fit glue & cramp together.
no other fixings reg for small motors
I used a 1" thick piece of Marine ply in an 'L' shape, secured to the horizontal and vertical with 1" clamps, through bolted with M5 countersunk screws and nuts. Holes drilled in situ to get the top horizontal. With the clamps you need the vertical clamped to prevent the weight of the outboard swinging down. Works well and just cost the clamps. You could also use M5 or M6 'U' bolts but I thought the clamps better and clamped the tube better.
Using your design, I would use two pieces of solid timber, possibly with the grains running at 90º, for strength. I find that solid wood stands up to weather better than ply, but I suppose if the ply is well protected it would be alright.
With my previous boat I used simply to clamp the o/b to the top pushpit rail and do a small lashing between the leg and the lower rail - worked fine. My present boat came with a proper o/b bracket to which I have added two sheets of aluminium chequer plate to protect the varnish from the o/b clamps.