Air taxi Captain reported a taxi deviation onto an overrun area of the runway. Reporter stated that the wording of the clearance; a lack of signage; and charting for that area were perhaps contributing.

Narrative

Revenue flight from LIT to ZZZ. Our assigned departure runway was 4L. During our briefing we discussed a NOTAM for the last 954 of Taxiway A closed due to construction and a Hotspot around Runways 4L and 36. We anticipated (Bias expectation) a taxi route of 'A' to 'A6'; then cross Runway 4L with either some taxiways on the opposite or a back taxi.Our clearance ended up as follows; taxi via 'A' to 'A6' plan to back taxi to Runway 4L. We briefed that and traced it out visually with both the GARMIN safe taxi and our Jepp taxi chart. Looking at the maps it appeared to be a simple task and the charts showed what appeared to be hard pavement" all the back down Runway 36 followed by a left turn onto 4L.After taxing out to 'A6' and holding short of Runway 36 we received the clearance to back taxi 36 and then cleared for takeoff on Runway 4L. As we entered the runway for the back taxi at our normal taxi pace the Tower controller asked us to pick up our taxi speed as there was an aircraft on final for 36. That caught my attention and I began scanning the sky for the inbound traffic to gauge how much time we would have. As PM I wasn't particularly thinking about our taxi route as we had briefed it and visually reviewed the charts and could see 'hard pavement' ahead all the way down to Runway 4L. As we were approaching the end of Runway 36 and starting to make the turn onto 4L I noticed objects rising above the pavement in front of us. I asked the left seat pilot taxing the airplane to 'STOP'. At this point we had exited Runway 36 onto what appeared to be the overrun area for Runway 22R and it contained runway alignment lights protruding from the pavement. We had already entered about half the area and were close to exiting on the approach end or beginning of Runway 4L when we stopped and it was we were on 'pavement' shared with the runway. At this point we briefed the objects to avoid and aligned with the runway for takeoff. No damage or 'near misses' with any objects took place.After a normal takeoff and during climbout I started asking myself questions. How did that happen? Was there a taxiway we missed prior to the end of Runway 36? Did we exceed the load bearing capacity of the pavement we were on?After going back and reviewing both the GARMIN safe taxi map and the Jepp taxi diagram it appears there is a taxiway; albeit very short; at the beginning of Runway 36 but it is difficult to see and not clear what the taxiway name is (i.e. Taxiway 'A'?). Also we were told to back taxi into position on Runway 4L; not back taxi and exit Taxiway 'A' to 4L. Between the poor mapping and lack of guidance/clearance this led us onto an area we should have been on.My recommendation is to share this with LIT; check the signage at the 'Hotspot'; and perhaps issue a chart better depicting this 'hot spot' and the threats."