Most triage advice assumes one account and a calm week. Here is what survives contact with four accounts and a bad one.
Start from Important, not from the top
The chronological inbox is the worst possible ordering for triage, because arrival time has no relationship to consequence. Open the Important label first. It is usually between three and nine messages, and it is the only part of this routine that is genuinely urgent.
Answer, don't plan to answer
If a reply takes under two minutes, send it now. Parrot's draft is already there, so the real cost is reading it and deciding you agree. Deferring a two-minute reply converts it into a five-minute reply later, plus the cost of remembering it exists.
Batch the rest by label, not by account
Work, Finance, Travel. Handle each label as a block across every account at once. The context switch between two invoices is cheap. The switch between an invoice and a customer escalation is not, and doing them in arrival order guarantees you pay it constantly.
Leave Updates for the afternoon
Newsletters, digests, and product announcements are not mail. They are reading. Give them a slot after lunch or skip them entirely for a week and see whether anything breaks.
Ten minutes, in that order, most mornings. It is not clever, but it holds.

