I guess with almost 800 candidates to choose from I will not get back any further on Peter Tullock (h).
A possible lead
In the British Merchant Seamens Records 1835 - 1857 is a Peter Tullock. His age at the start of the record is 33, so he was born c. 1802. His place of birth is given as Larwick (Lerwick)
The reason I think this might just possibly be your man is that several of his voyages were made in a ship called the Astley. Astley was the family name of the Delavals of Seaton Delaval, a mile or so inland from Seaton Sluice, and they were major landowners in the area. A ship called the Astley was apparently launched at Seaton Sluice in February 1826 (Durham County Advertiser), and there are records of it in the newspapers throughout the 1830's, its home port being Seaton Sluice
The final voyage in the record is dated October 1839 on the Lady Combermere and below this is, I am pretty sure, is written S. Sluice. There are quite a few references in the newspapers to the Lady Combermere sailing to various destinations and its port of origin is given as Seaton Sluice.
So - I think there's a possibility this could be him
If so - you have a possible place of origin.
There is the death of a Peter Tullock aged 50 in Gravesend in the 4th quarter of 1853. Given that the ships he served on were colliers engaged in mainly coastal trade, there is a vague possibility that this might be him?