Pilot reported a conflict with another aircraft while taxiing to parking. Informal airport procedures and a lack of radio equipped aircraft were cited as contributing factors to the incident.

Narrative

I was solo in a rented J3 Cub. After completing 4 laps in the traffic pattern; I landed on Runway XY at ZZZ. There was a plane behind me on final; and a plane holding short of the runway. My plane; and the other planes that were in the pattern; are not equipped with radios. After my last landing; I vacated the runway to right and taxied parallel to the runway parking. I was roughly 1300 feet down the runway when I exited. Soon after exiting; I first heard a plane and then noticed it about 300 feet away and 100 feet high at my 1-2 o'clock. It had taken off on Runway XXG. I continued my taxi and parked the plane near the fuel pump.There is a procedure in place to prevent this. It's not published by the FAA; rather posted at the field. XZ/XY is the primary runway; and [runway] XXG ('glider') abuts it. XXG is published in the AFD for use by gliders and based aircraft operations only. The procedure calls to keep out of the end of XXG near where it touches [runway] XZ/XY. For landing short on XY; you cross XXG perpendicularly after clearing it. For landing long XY like I was; you continue long and then turn right perpendicular to the fuel. Because of the topography and trees; a plane taking off on XXG or XY could not see each other. I had foolishly vacated the runway early and went through; by my best estimation; the last third of the hotspot. I was familiar with this procedure. My instructor emphasized taxiing to the runway properly; and told me about the accident that led to the creation of this procedure (I trained for my tailwheel only at this airport). During my training; proper procedure for taxing to the runway was emphasized. Proper exit procedures were not emphasized. The 'hot spot' itself wasn't emphasized particularly well either.The primary factor in this was my lack of awareness of proper procedure. I should have known the procedure. However; even if I had continued on the runway; though; there would still have been a traffic conflict; and if I had come in just a moment sooner; I would have been almost directly overflown. Another factor was the plane behind me. It was rather close; and because I hadn't been able to see it since base; I really had no idea how close behind me it was. Because of the informality of the field; some people choose to cut things a little close. I wanted to get out of there was as soon as possible and not loiter on the runway. Another factor was my lack of vigilance. I had completed my 3rd flight in the plane solo safely and flown very well; and I did not consider the threat of [runway] XXG. It's not over until it's over. Another factor was the poor judgement in the pilot deciding to use [runway] XXG. There were 3 planes in the pattern for [runway] XY. It was clearly the active; and is used almost exclusively. In fact; before this moment I had never seen a plane on XXG. Related to this is a procedure that allows for this. There is still incredible potential for a midair collision even if both planes are following the procedure. If the plane taking off on XXG had taken off just a minute later; it might have conflicted with plane departing XY. There is absolutely no visibility between the two runways. Other than convenience (it's closer to parking); there is no reason a power plane needs to use XXG. Another factor was the lack of radios. In my limited experience at the field; things generally operate relatively smoothly without radios. However; radio communication would almost certainly have prevented this.