Many of the runes affect (or should affect if character emulates their god) the rune holder's personality in a way that is described in the HQG. Not all the rules need the description or guidance but there are some runes that do not have a description and I thought that it would be interesting to have it. I like Harald's response below and have adapted it to my campaign.
I added also one for Unlife rune
"soulless, fiendish, relentless, cold"
Moon and Light rune would perhaps benefit of personality traits. What have ascribed to them if you have done so...
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Harald Smith responded like this in the Glorantha forum for Law and Spirit:
While there isn’t a formal ‘personality’ for Spirit and Law, those tend to lead the character towards certain magical outlooks that could easily be described as part of their personality.
Law logical, rigorous, materialistic (as in desiring to use/manipulate the runes/magic to their own ends), judging (or judgmental)
Spirit ecstatic, spiritual, connected (with the spirit world), aware
And your players can probably riff on those thoughts to align with their characters.
As for Communication and Illusion together – sounds like someone who might be smooth-tongued, lying, etc.