all referring to a lofty state, as indicated by the letter L present
in all of these roots.
So, I think that דֶגֶל DEGEL refers to the entire system of a
painted sign, an אות OT, lifted upon a tall
pole (Hebrew: תורן TOREN = T-OREN, a variant of the tree name
אורן OREN.)
The extra-biblical דֶקֶל DEQEL, 'palm tree', is in shape a kind
of a דֶגֶל DEGEL:
a tall trunk capped by a shock of long fronds.
In Song 5:10 we find דגוּל DAGUL in the sense of 'outstanding,
over-towering'.
In Song 2:4 we find דִגְלוֹ DIGL-O, which I doubt means 'his
banner'.