Hi,
not my family-line at all so probably nothing of substance to add beyond what you probably know, but;

In those days Cardiff was an extremely busy sea port, the docks were built to handle the vast output of the South Wales coalfields. An important part of this coal was high-quality "steam" coal from the Rhondda Valley, also called "sea" coal, as it was the preferred coal for use in steam engines, particularly steam ships and railway locomotives. Hence ships from across the world visited Cardiff and nearby Penarth and Barry docks, especially during the late C19th when the world's navies were building more and more steam-powered warships as well as merchant ships, all of which needed Welsh steam coal.
https://en.wikipedia.org/wiki/Cardiff_Docks

For ships to access these docks they needed good seamanship and top local pilots, as the Bristol Channel and Severn Estuary is renowned for it's treacherous waters due to the strong tidal race etc. Some say this is why the Cardiff dock front became known as "Tiger" Bay.
http://www.urban75.org/photos/wales/cardiff-bay-docks.html

So, if Jacob was a good enough sailor to be a pilot, then it's likely he'd have been able to gain work easily, and would have travelled all around the Severn estuary, which remained an important waterway to Gloucester and the Midlands well into the C20th. He'd have known the ports of Cardiff and Lydney well, and Tidenham too. It was also the norm for a son to have literally followed his father's footsteps, working since a boy, so it's possible Theodore met Nellie at Tidenham.
Then again, at that time several Forest of Dean miners were moving to South Wales for work, and vice versa, were there any miners in Nellie's family ?.
I see Nellie was in Cardiff when she died (young,sadly !), presumably Theodore was based there for his work ?.

As you know the Norwegians are renowned sailors since ancient times, browsing the net I see the name/word "Birseland" associated with Glasgow and the River Clyde, which was the centre of world ship-building in the early C20th, and a very busy port in itself; the city still has very strong connections with Scandanavia and beyond especially thro' sailors and their families. I have no doubt your Jacobson ancestors would have known Glasgow and the Clyde.

I don't have worldwide access to Ancestry, but FamilySearch has several Norwegian records, clearly the name Jacob Jacobsen is a very common one across several families and generations, hopefully you've been able to research that further than I can !
I suspect the Birseland (Birceland) is linked to Birkeland, there are a few places and people in Norway of this name.
https://en.wikipedia.org/wiki/Birkeland

Searching the family in the Census,

1891 Pearl Street, Roath, Cardiff, Glamorgan.
Given Name Surname Relationship Age Estimated Birth Year Gender Birth City Birth County Birth Country
George Carey Watts Lodger 32 1859 Sailor Male Westbury on Severn Glamorgan Wales
George Hobbs Lodger 28 1863 Male Labourer Christonsore Norway
Ellen Jacobson Lodger 24 1867 Female Chepstow, Tidenham
Theodore Jacobson Head 27 1864 Sailor Male Plymouth Devon England

Pearl Street isn't far from the Docks. The rest of this Census page includes several sailors and mariners, with many giving ports at home(Cornwall, Southampton, etc) and abroad as their places of birth, perhaps these were rented houses ?. I see that Theodore was "born in Plymouth", and wife Nellie is using her formal name of Ellen, short for Eleanor ?. I guess it's not a coincidence that they have a Norwegian lodger.
(By unhelpful coincidence there is another Theodore Jacobson in the 1891 Census, born abt 1867, the Master of a Norwegian-crewed & registered schooner "Liberal" currently visiting Boston, Lincolnshire. In fact, there are several Jacobsons shown on Ancestry in the UK Census' of the late 1800s, all in ships or seaports, particularly in the 1881 Census. However I cannot yet find our Theodore in 1881, maybe he was at sea ?).

It looks like Theodore remarried after Nellie's early death, here he is in 1901 with a new family, maybe suggesting a second marriage in abt 1892 ?.
I THINK this is our man, but an odd change of occupation perhaps ?.

1901 44 Cornelia Street, Roath, Cardiff
Household Number Given Name Surname Relationship Age Birth Year (Derived) Gender Birth City Birth County Birth Country
Theodore Jacobson Head 36 1865 Erector at iron works Male Norway
Mary L Jacobson Wife 35 1866 Female Cardiff Glamorgan Wales
Randolph Jacobson Son 8 1893 Male Cardiff Glamorgan Wales
Hilda Irene Jacobson Daughter 6 1895 Female Cardiff Glamorgan Wales
Leonard V Jacobson Son 4 1897 Male Cardiff Glamorgan Wales
Dorothy J Jacobson Daughter 2 1899 Female Cardiff Glamorgan Wales
Winifred K Jacobson Daughter 10 Months 1900 Female Cardiff Glamorgan Wales

I now find that Theodore married Mary Louisa Falle in Cardiff in late 1900, so presumably these children are all from his previous marriage to Nellie in 1890 ?.
(I also wonder if "Falle" is a Norwegian name ?)

Or have I got this all wrong ?!...

I cannot find Cornelia Street on modern maps, according to this book it was built in abt 1890, by the Dowlais Ironworks Company, in Roath/Splott so not far from his Pearl Street address. Presumably this newly-built house was a perk of his job ?.

https://books.google.co.uk/books?id=nnQ7AwAAQBAJ&pg=PT87&lpg=PT87&dq=cornel...

Ref Dowlais Ironworks, this company's origins were in Merthyr Tydfil (where the best steam coal was mined). If (I'm still not certain) this is indeed the right Theodore, then it may explain why the records show he died in Merthyr in early 1934, aged 71.

"the Dowlais Works' early conversion to steel production allowed it to survive into the 1930s. However, largely as a result of the Great Depression, the main works ceased production in 1936, the company having built a new iron and steel works at East Moors, adjacent to the docks at Cardiff in the late 19th century."
from
https://en.wikipedia.org/wiki/Dowlais_Ironworks