Hi Keith
I have returned with an answer but probably not the one you were hoping for.
In 1900, the resident was Joseph Jones.
From 1901 to 1903, the resident was Edward Angus.
No-one was listed for 1904.
From 1905 to 1915, Joseph Jones (again, presumably) was at this address.
The Birkenhead Electoral Roll has three divisions for each ward; the 'main' list, a lodgers list and a service list (and I assume this is standard across the country).
I made sure I checked all three divisions but no mention of the Thelwells I'm afraid.
I'm sure there's only one Cathcart Street but just to confirm, the one I checked was in Birkenhead Grange Ward.
'Grange' should be visible on the Enumerators List on the census.
I've come across this problem before when researching my own family - maybe for whatever reason he wasn't eligible to vote, or chose not to be eligble?
Women didn't get to vote until 1918, and then only when over 30 years old.
I guess that Joseph Jones isn't on the Census for the address?
Let me know if I can do anything else.
Neil