I'm installing linear pull brakes on a rickshaw bike and the back brakes both have a left arm with a noodle holder. Shouldn't one of the wheels have a reversed right hand noodle holder for the inner cable lead?

Nope. Arm with a bale (noodle holder) on the right front side of the bike. Arm with a bale on the left rear side of the bike.

The front one will be the left arm while viewing the bike from the front, however. The typical V-brake set will be for front or rear use.

Here are pics, sorry the rear one is so blurry.

There may be a linear pull brake with the arms reversed but, if one exists, they're rare.

If front cable routing on left side of bike is crucial, I think Odyssey 1999 caliper would work if fork is drilled for a caliper bolt and has mtb/cruiser brake reach.

They're weaker brakes than most Vees, and also require a short pull lever to go with 'em.

Cane Creek Used to make 2 lines, 1 was a top of the range direct pull brake that could be assembled
to have it operate from either end . by flipping over the arms so housing stops could be on either side

But now they seem to only offer this one Cane Creek Direct Curve 3 Brake (Single)

so, now you may need to find old stock or win an auction.



Magura's Hydraulic rim brake , HS22 or HS33 may be both more versatile and powerful.. they mount on V brake Posts