Aeronca 65-C pilot reported failure of the right brake resulting in a runway excursion during landing. Pilot taxied back onto runway.

Narrative

Day 0; I was relocating my Aeronca Chief (65-C) to ZZZ to perform the annual inspection on it (which is due the next month). I noted NO discrepancies on departure; the airplane ran great; taxied and took off with no issues. Contacted ZZZ [Tower] to obtain a landing clearance; reported the left base for runway XX; was cleared to land. I performed a wheel landing touchdown; as the tailwheel touched the ground; the airplane started drifting left; I applied full right rudder but it was not enough to maintain centerline. I then tried applying R/H brake to maintain centerline but the puddle went to the floor with no noticeable braking action. At this point I was drifting to the grass and saw a landing light getting close; so I decided to apply left rudder to increase the turn to the left to avoid impact with the landing light. I continued the left turn to taxi back onto the runway. At this point it was (at best) a high-speed taxi. I obtained a taxi clearance with the tower explaining I had no right brake. After shutdown; I contacted the airport manager Person A; he arrived shortly after to inspect the aircraft for damage. He and I noted Zero damage; no impacts of the wings; propeller; etc.; we contacted the tower to ask if they needed anything. They were good with Person A's findings and statement. Person B and I decided to look into the brake system and found the brake rigging was getting loose thus the mechanical cables were not able to apply much if any pressure to the brake shoe cam on the R/H brake assembly.