C172 student pilot reported a right brake failure during landing and subsequent taxiway excursion.

Narrative

On Day 0; I was scheduled to conduct a solo cross-country flight from ZZZ to ZZZ1 with a stop at ZZZ2 on the way back.Upon checking my brakes during the initial taxi; both had pressure and stopping force; however; I did notice the right brake felt slightly softer than the left. Given my experience thus far; I did not find this to be of concern. I've felt this sort of difference on other planes I've flown during my training and considered this to be normal variation. I also recall checking the brake lines and sweeping my hand underneath the calipers during the preflight inspection and did not observe any visible brake fluid. Flights from ZZZ to ZZZ1 and ZZZ1 to ZZZ2 proceeded without incident or concern.After landing at ZZZ2 at XA:26 on Runway XX; I noticed the right brake felt softer than before; while exiting the runway at Taxiway 1; so I pumped the breaks several times to build up some pressure and was able to taxi back for an eastbound departure to ZZZ without issue. I departed ZZZ2 at XA:37.On my straight-in approach to ZZZ the controller switched me from XXR to XXL. I accepted the landing clearance and landed without issue on XXL at XB:01. After touching down; I applied the brakes and noticed the right brake compressed nearly to the floor. The plane deaccelerated a bit slower than typical without the full right brake; so I chose not to exit the runway at Taxiway 1 as I was still carrying too much speed. I held the brake all the way down and kept backpressure on the yoke to help slow the plane down. I exited the runway on Taxiway 2 with full braking authority on the left brake; which kept me centered on the taxiway during the left turn; but when I applied the right rudder and brake again to stop the plane clear of the hold-short bars there was very little braking action. The plane continued to roll forward and to the left as I pumped the right brake attempting to slow the plane and center it on Taxiway 2; but there wasn't enough braking action to prevent the left main from drifting off the taxiway as I came to a stop. I proceeded with switching to Ground and requested a taxi clearance. Once granted; I check Taxiway 3 to confirm it was clear and applied the throttle to continue down Taxiway 3. As the plane moved forward; I recall hearing a pop and notice some blue glass shards in my periphery. It was at this moment that I realized that I had struck the lens of a blue taxiway edge light. I'm not clear if the left main or left strut contacted the lens sending it into the propeller or if the propeller contacted the lens first; either way; it was evident that the propeller struck the glass lens. I was able to slowly taxi the plane back to its parking spot using a pumping action to make the right turns at Taxiway 4 and the parking isle.This event taught me the following lessons learned.- A difference in brake pressure between the left and right peddles during a brake check should be considered abnormal and warrants further investigation.- If the plane ever strays off the taxi surface; the plane should be shut down so the path to get back on can be inspected.- I recently learned Ground can be contacted to notify them of the situation and to request a tow back. This would have been preferred over continuing taxi operations. Especially if there is a known deficiency; which could potentially hinder controllability during ground operations.- At the first hint of a control difficulty; action should be taken to secure the plane and to inspect the problem.- External or self-imposed pressures contributed to this incident and include finishing the XC flight; changing runways on the approach; exiting the runway expeditiously; getting the left wheel back on the taxiway as soon as possible. These pressures could have better been managed by committing to preferred alternatives such as finishing the flight later; telling ATC 'unable'; or using whatever time is needed on the runway/taxiway.