It is better to understand conditional sentences with different moods associated with the condition and the proposition, as in French.
In French, the equivalent of “if I were you, I would do something” is “Si j’étais vous, je ferais quelque chose”. The condition is in l’imparfait and the proposition is in le conditionnel. It is important to not confuse the moods used in each part.
Comparing this to English, I would say the conjugation for the past subjunctive is always the plural past tense form or (for the past subjunctive perfect) the past perfect tense form, and the conjugation for the conditional is “would + infinitive” or (for the conditional perfect) “would have + past participle”. Sometimes one can replace “would” with other modal verbs, e.g., “could” and “might”. And the second conditional is “if past subjunctive, conditional”, and the third conditional is “if past subjunctive perfect, conditional perfect”.
It seems to me that it is always required to use a modal verb in the conditional mood.
There is also a present subjunctive mood in English. You may or may not use a modal verb in the present subjunctive mood, examples are:
- God bless you.
- May the force be with you.
- He suggests that she finish her homework before hanging out with friends.
- He suggests that she should finish her homework before hanging out with friends.