Ugh what?Sword and board came into it's own the better armour got, in cultures with lesser metalworking skills and lighter armours, 2 weapons are far more common. It has more to do with tactics, technology and training (the 3 essential Ts!)
Shield in pretty much all cases became less used anytime when someone had really good and covering armor.
Show me one source about "lightly armored and poor equipped" guys with "2 weapons.
Because from what I've ever seen, from poor Celts trough Germanic people trough Persian Empire in antiquity, Vikings/Nords Slavs from all the Europe Japanese peasants, and whoever else, shield, often big one is natural and obvious way of the warrior, to protect oneself and engage opponent.
Before Renaissance, any hints at "TWF" are episodic at best.
If you're talking about scenes from Agrippa, DiGrassi etc. works, then :So then why did you have things like the Florentine style of fighting? It might not have been common, but it was used.
1) It's civilian context - so as mentioned, daggers and whatever indeed serve as "poor version" of sword'n'board.
But backing to homebrew, from this huge offtop - some of those scarse ideas about fighting with two weapons may easily serve as good inspiration for TWF to work in fantasy...
Indeed, the very fact that someone had used them in real life, at least in training to check out the concept, gives 'green light' for some RPG archetypes.
Maybe hitting with 'off hand weapons" gives some bonuses to attacks with the "main"?
"For every single successful attack with off hand weapons threat range of main hand attack is doubled. This bonus applies only to attack made during the same Full attack action".