た ほうがいい

What you say is... kind of true, but not very useful. In this case, it's the た form is not really 'past tense' - tense is generally determined by the last verb in a sentence.

In the second place, while the most basic and literal meaning of 方（ほう）is 'direction', it also has a meaning of 'method'. (It's sometimes translated 'way' in order to preserve that ambiguity). In this expression, a meaning like 'method' or 'manner' is the more important one.

It -is- useful to pay attention the last bit you noticed, the fact that this が is the subject marking particle and this いい is the adjective 'good'. (You could in fact change it to other adjectives, to say that taking a certain action would be wise or dangerous or whatever.)

You could say 休んだほうがいい literally means 'the resting way is good' but that's not very natural, and ほう here is only acting as a grammatical marker. Translating it as a word in it's own right is heavy-handed.

'It would be better to ___' is a popular translation because it avoids the problem of context changing the meaning around, but the vast majority of the time it's a mild suggestion along the lines of 'I think you should ___' but
less forceful, perhaps most naturally translated as 'Why don't you ___?'

(Of course, depending on context, 'I think' and 'you' may not be accurate.)

Anyway, the take-away is - you're better off to understand set grammar patterns as set grammar patterns and not try to work out the exact words. It would be more effective to think of (v-past)ほうがいい as a complex conjugation that creates a suggestion than to try to remember all the different words and particles and put them together when someone's talking at full speed.

What would the literal translation of たほうがいい be? "た" is pass tense, and "ほう" means direction, and "がいい" identifies what is good. So たほうがいい would mean "In the direction of [insert past tense verb] would be good." I hope I got that right. Correct me if I'm wrong.