SLDF Brigades were 3 Mech 1 Infantry for a Mech unit and 3 Infantry 1 Mech for the Infantry IIRC
Not quite.
SLDF Divisions had 3 line brigades of 3 regiments each. 'Mech Divisions had 2 'Mech and 1 Infantry, Infantry Divisions had 1 'Mech and 2 Infantry. Each brigade had 3 regiments of that type.
However a brigade was not usually a deployment unit, it was an administrative one. Typically if a force smaller than a brigade was needed, a composite force mixing 'Mechs, Infantry and other arms was formed for the purpose.