I searched the Naval History Website using the search engine on the home page and found several entries for a vessel 'HMS Sagitta'. It appears to have been a naval sloop in service in the Med and Red Sea and was sent on active service. I also found an image of the vessel which could be your father's vessel. My father served on HMS Dido which mentioned alongside one extract relating to the Red Sea port of Massawa.
Entries found :
"SAGITTA (has been found spelt SARGETTA), hired yacht, Pendant No 01. Built 1908, 744grt/758TM. Armament: 2-12pdr, 1-6pdr AA. In service 5.12.14-15.2.18. May have served as wireless-equipped A/P Group Leader or in special yacht squadrons, at home or in Mediterranean. Battle Honour (and link to despatches, casualties, awards) Belgian Coast 1915. Served in WW2.
Royal Navy Auxiliary Patrol ships of World War 1, based on British Warships, 1914-1919 by Dittmar and Colledge
Red Sea Monday 20th July 1942
4. ARPHA and SAGITTA sailed for the Yemen coast to intercept German and Italian refugees who were due to leave Jedda on the 22nd July. This was a result of political pressure on Ibn Saud, who agreed that these internees could leave and that he would connive at out ships intercepting them inside territorial waters.
5. ROBERTS was moved from Suez to Abu Zenina anchorage for the protection of shipping waiting call up to Suez.
Red Sea Monday 3rd August 1942
3. H.M.S. SAGITTA intercepted fourteen Italian escapees from the Yemen at Sherm Makar. No objection was raised by the local authorities to H.M.S. SAGITTA's presence in territorial waters.
Red Sea
13. DIDO was docked in the Admiralty Floating Dock at Massawa for repairs to her plates aft.
14. Nineteen Italian internees were intercepted by ARPHA and SAGITTA off the Yemen Coast south of Jedda."