12/30 isn't of great benefit to EDI for a variety of reasons including the lack of ILS, poor alignment to prevailing winds, noise issues and potential conflict with any traffic using 06/24 and nearby taxiways.
Aircraft cannot land on runway 12/30 or take-off from runway 30 if there is any potential conflict with aircraft using 06/24 or adjacent taxiways e.g. in the event of a missed approach, go-around, over-run or simply the fact that the traffic using the two runways cross each other's paths. Departures from 12 don't cause such conflicts so these used to occur quite frequently up until at least the 90s, especially turboprop aircraft which had less of a noise footprint.
If I understand the NATS data correctly
NATS | AIS - Home , the decision height for the non-precision approach to runway 30 is about 1,900ft, which is about 5 or 6 miles from the threshold and 5 miles from the EDN NDB, due to the proximity of high ground at Hillend.
Decision height for the non-precision approach to runway 12 is 790ft (about 2 miles from threshold) due to towers / masts, presumably including the Forth Road Bridge.
On 13th October this year, 06/24 was supposed to close at 23:00 (BST) for overnight maintenance works. Nine passenger flights were inbound and expected to arrive between 23:00 and 23:55. Cloud-base was broken at 700ft and overcast at 1400ft with 12km visibility and a 10kt crosswind (040 degrees) on runway 12. I doubt whether many of the inbounds (which included a BA B763) would have attempted a non-precision approach to runway 12 in these conditions and, even if they had, I suspect that the chances of a missed approach would have been very high unless they got lucky with a break in the clouds. I suspect that airlines have policies that would discourage or prohibit a non-precision approach in such conditions but I'm not an expert on this matter. Maybe if any professional pilots are reading this they might be able to comment on whether these conditions would be below their airline's minimums for a non-precision approach or whether they would fly an approach in the hope of sighting the runway before reaching decision height.
Whether due to weather or for other reasons (I'm not sure which) 06/24 remained open to accept all of the inbounds.
In the early hours of 13th October, the Thomson B738 from Sharm landed on runway 12 at about 03:45 (BST). If 12/30 is closed permanently as a result of the new stands at Block 33, I wonder whether that was perhaps the final fixed wing aircraft ever to use 12/30?