It transpires that there are three Royal Naval casualties from Patrol Vessel 4 recorded by the CWGC for the 29th November, including two officers:
Royal Navy Personnel
Lieutenant (E) George Percival Harding Aged 58
Lieutenant Reginald Henry Whiteley Aged 49
Ordinary Seaman John Caleb Mitchell (MiD) D/BD/X 1750 Aged 22
OS John Caleb Mitchell was awarded a posthumous MiD, the London Gazette entry for which reads:
For gallant conduct in action against the enemy:
The Distinguished Service Medal.
Seaman Edgar Leo Toms, R.N.R. X.I9222A.
Mention in Despatches (Posthumous}.
Ordinary Seaman John Caleb Mitchell, R.N.V.R., D/BD/X.I750.
It's unclear whether Seaman Edgar Leo Toms was also a member of crew of Patrol Vessel 4, or how many crew, both RN and civilian, Patrol Vessel 4 had, or who it was who recalled the actions of John Caleb Mitchell, which resulted in his posthumous award.
The record of L G Shannon's death shows three other civilian deaths from Patrol Vessel 4
J Dick - Poole
A Moore - Poole
A Spurriet - Poole
1939 Register shows L G Shannon as a General Worker, rather than a merchant seaman, so whether this reflected his longstanding situation, or was just how he came to be recorded on the day I couldn't say. Is there any knowledge within the family of his always having been a seaman?
I have found no mention of Pilot Vessel 4, Patrol Vessel 4, Stoomloodsvaartuig 4 or Hellevoetsluis in British Vessels Lost at Sea 1939–1945. I think this reflects a general trend, in that foreign vessels crewed by Royal Navy personnel, in whole or in part, will tend to be cited in Commonwealth War Graves Commission records for casualties, as well as in records of awards, but if the vessels are lost, they are not recorded as British war losses. For example, there were a number of French submarine chasers, called Chasseurs, which were out and out military vessels crewed by the Royal Navy, and which are seen as an element of Coastal Forces, and recorded as such by us, for which there are some 28 RN casualties recorded from 5 of them at various times. But those which were sunk, to not appear in any record of vessels lost, even when their crews are.
I suspect the story of how this vessel came to be in Britain in 1940, and what happened to its original Dutch crew will lie in Dutch records, whilst what happened to Patrol Vessel 4, is likely only to be found in such documentation as may still exist in the Public Record Office at Kew, for the award of Mention in Dispatches (Posthumous) for John Caleb Mitchell. You could run the matter past the Royal Navy again, but ask about Patrol Vessel 4, rather than Pilot Vessel 4, just in case that may make a difference.