As someone who does not exactly understand how naval commissions worked in the 18th century, I am curious to know if there might have ever been an occasion where a commissioned officer (such as a First Lieutenant) would sail on a merchant vessel or civilian ship? Is it possible that they could have been stationed on a vessel that was in a different port and needed the transportation? Or would they ever sail on a civilian ship while on furlough?
At it's simplest, the answer is yes, commissioned officers could sail on vessels that weren't warships.
In times of war, the Royal Navy would supplement its own warships with merchant vessels to perform roles that didn't require a warship, such as, transportation (of soldiers, horses, military supplies and victuals, etc.) In these cases, the RN would hire merchant ships, including their crews, but would put a RN officer in charge. In almost all cases, this would be a lieutenant, who would become the ship's commander (and he would receive a Navy commission to do so).
There was nothing stopping an officer from travelling on a merchant vessel as a passenger. If an officer was assigned to a ship on a foreign station, he would be expected to make his way there with reasonable haste. Often he could take passage on a warship that was making its way to the station but in situations where this wasn't available, the use of a merchant ship would be a valid option.
An officer without active employment (i.e. without a ship) was placed on half pay. Such a situation could make life fairly uncomfortable for a junior officer since half pay might barely cover their family expenses. However, they were not free to take other jobs during these gaps between commissions since (in theory) they could be called up at any time. Having to reject a commission because they were working on a merchant vessel would have serious consequences for their naval careers. Therefore officers who struggled to make ends meet would often resign from the Navy in order to start a career elsewhere. While it might be possible for them to re-join the Navy at a later date, their career prospects would be poor, since they would drop to the bottom of the list for promotions and commands (which were based on seniority).
Nelson's Navy, The Ships, Men and Organisation, 1793-1815, Brian Lavery (Conway, 1989)
A Social History of British Naval Officers 1775-1815, Evan Wilson (Boydell, 2017)