Etymology of 'doylum'
Solution 1:
Yaron Matras, in his 2010 Romani in Britain: The Afterlife of a Language has this entry...
fool n. doylem ER dinilo; Yiddish goylem
(ER = European Romani)
From Wikipedia: in Modern Hebrew, golem is used to mean "dumb" or "helpless". Similarly, it is often used today as a metaphor for a brainless lunk...
The Yiddish origin is also given here, but that's a page on the University of Manchester's site, where Matras is a Professor of Linguistics. I believe him though, even if he's the only authority I can find.
Solution 2:
And yet another meritorious source:
Yorkshire Words Today : A Glossary of Regional Dialect (1997), page 41:
DOYLEM n simpleton (?derived from doychle) WR cf. EDD doychle Sc, also written doichle, 'a dull stupid person; a sloven', also 'to walk in a stupid, dreamy state'; cf. EDD entry for the West Country word doll, 'to talk foolishly, distractedly', and OED dolled, dollt, 'stupid; foolish, crazed; affected in mind'.
Solution 3:
There's also the spelling doylem. I shouldn't dabble in this one, but I will say that I find it interesting that Doyle stems from Irish Dubhghaill (ˈd̪ˠʊwəlʲ), dubh "black" + gall "stranger", and that that term was used by the Irish to desribe "new foreigners", who had darker skin than them and who arrived during Tudor conquest of Ireland [wiki]. In some languages, foreigners have been known to get a label "the mutes" by the locals, because they'd speak a language no one understood, and also they couldn't understand a word of the language of the locals. Another word for mute is dumb, which idiots are.
Edit:
Someone's given an up vote, do keep them coming, but bear in mind that this is hardly more than folk etymology.
Solution 4:
'Doyle' a local term of endearment indeed and local colloquialism - I have grown up in Hartlepool (75 Miles North of Leeds) and still reside there now in my 48th year. And to this day I still use the word 'Doyle' for someone who is daft, fool or idiot, mainly to friends, so the word is very frequent in our everyday vocabulary.