In the past a number of people have suggested that the identity for the aircraft is Lockheed Model 12a "Electra Junior" LA622 / 42-38350 but nothing at the crash site fits with this being a Lockheed aircraft. I will however detail the aircraft suggested and show what information I have found surrounding 24 Squadron's VIP flights around the period of the accident at Coniston on this page.
Leaving aside the evidence at the crash site for the time being there are now two items of documentary evidence that it was a "Beech" aircraft involved. Firstly the Lockheed Overseas Corporation annual report mentions the incident as involving a Beech aircraft and surely Lockheed themselves would not make the identification error for that of a Lockheed Electra. Secondly the Ayr Station record book mentions the aircraft type as being a "Twin Beech" which was the nick-name for a Beechcraft Model 18 and the scribe at Ayr would surely have know the aircraft types flying in and out of the base. I have found no contemporary evidence of anyone recording the aircraft type as being a Lockheed Electra. I have also visited the crash site of a Lockheed Lodestar which was a military variant based on the Electra family. Nothing at the Lodestar crashsite looks like anything at the Coniston site.
Having said that I feel it correct to detail the history of the Lockheed Electra 12a suggested and it reads as follows; it was taken on charge by the USAAF as a UC-40d variant on 14th March 1942 and was given the US Military identity of 42-38350, it was then transferred to the UK under the Lend-Lease program on 4th April 1942 and given the UK RAF identity of LA622. In the UK it was initially taken on charge with the "USATO" (Abbotsinch) on 12th May 1942. The "USATO" was probably the USATC (United States Air Transport Command). On paper it was transferred to 24 Squadron at Hendon on 19th May 1942 but this transfer may have actually never happened on that date as it was being used by 24 Squadron up to the end of July 1942. Here there is a gap in the history until it was was struck off charge by the RAF on 30th November 1943.
I have bought 24 Squadron's ORB for September and October 1942 and LA622 to check if it was being flown by them around the time of the Coniston accident. It was not flown by 24 Squadron at all during this period. It may have either been grounded by then or being used by the USATC. By the time it was struck off charge in November 1943 it could have been damaged at any point after July 1942 or it may have just been a worn out aircraft by November 1943. Theoretically it is possible that Lockheed 12a LA622 was the aircraft that crashed into the Old Man of Coniston on 14th October 1942 while on charge with the USATC but evidence at the crash site does not lend weight to this being the aircraft.
During the period when Rickenbacker was in the UK in late-September to early-October 1942 and when the accident occurred at Coniston 24 Squadron flew various top brass of the military command around the UK, I suspect some were also involved in meetings with Rickenbacker. The flights involving high ranking officers were as follows:
On 26th September 1942, Maj Gen Young, Lt/Col Kendall, Lt/Col Goforth, Lt/Col James, Maj Charlebol, Capt Goodwin, S/Ldr (William Herbert?) Wetton from Prestwick to Hendon (this was the day after Rickenbacker arrived in the UK.)
On 26th September 1942, Sir Archibald Sinclair & Sir Louis Greig from Hendon to North Coates, Church Fenton, Fairlop and returning to Hendon.
On 27th September 1942, Mr H Morrison, Mr Watkins, Mr Taylor, Dr Wellington-Keo from Ringway to Hendon.
On 30th September 1942, ACM Frederick Bowhill, G/C Powell, G/C Dean, W/Co Jeffs from Hendon to Prestwick in morning and returned to Hendon with Mr Attlee, Mr McDonald, Mr Jenkins, Mr Clutterbeck in afternoon.
On 30th September 1942, W/Co Moore, Mr Miller, S/Ldr Maynard, W/Co Adams from Hendon to Prestwick in morning and returned to Hendon with Col. Ben, Lt/Col Cooke, F/Lt Coffart and Mr Jones to Hendon in afternoon.
On 2nd October 1942, Cpt Youell (Alan Bruce Hamilton Youell?), Mr Hildred, Mr Wormsley, Mr Lorning from Hendon to Prestwick.
On 3rd October 1942, Sir Archibald Sinclair, Sir Louis Greig, Sir Robert Watson-Watt from Hendon to Defford.
On 3rd October 1942, Lord Sherwood and Lord Corobray from Hendon to Scampton then to Grantham, Langar and Odiham before returning to Hendon, picking up Lord Cowdray at Odiham.
On 6th October 1942, Gen Sir Frederick Pile, Rt Hon H (Herbert?) Morrison, Sir H (Harold Richard?) Scott, Mr Peterson from Hendon to Gosport and back to Hendon.
On 8th October 1942 (when Rickenbacker left the UK), A/Cdr Storrar, Mr Cornelly, Mr Dismore from Hendon to Prestwick and return to Hendon on 9th October 1942.
In addition there were numerous flights to Belfast.