Does dressing well actually help?

Yes. If an airline has to perform an 'operational upgrade' due to an oversold economy cabin, they look for solo travelers who are dressed neatly and have high-tier frequent flyer status.

Should I ask at check-in or at the gate?

Ask at the check-in desk, but the gate agent has more authority. The gate agent is the one who officially processes seat changes after the flight closes for boarding.

Is it worth buying an upgrade if I have a short flight?

If the flight is under 3 hours, probably not. Unless the upgrade gets you lounge access and priority boarding, save your money for your destination.

How to secure a last-minute business class upgrade

Check for upgrade availability 24 hours before your flight by logging into the airline’s app or website. If no automated upgrade is offered, arrive at the gate 90 minutes early and politely ask the gate agent if any unsold business class seats are available for a cash or mile-based upgrade.

Check the seat map. Log into your booking via the airline's website or app. Look at the seat map to see if business class is mostly empty. If there are 5+ empty seats, your chances of a last-minute upgrade are high.
Monitor 'Upgrade' sections. Many airlines have an 'Upgrade' or 'Manage My Booking' tab. If the airline allows 'bid' upgrades, place your bid at least 48 hours out. If you are within 24 hours, look for a direct 'Buy Up' offer.
Use airline miles strategically. If you have status or miles, check if you can use them to jump the waitlist. Do this via the 'Manage Booking' portal before you even head to the airport.
Ask at the gate. Dress neatly and arrive at the gate 90 minutes before departure. Once the gate agent settles in, approach them quietly and ask: 'I’m looking to upgrade to business class today. Do you have any last-minute seat availability for purchase?'

Does dressing well actually help?: Yes. If an airline has to perform an 'operational upgrade' due to an oversold economy cabin, they look for solo travelers who are dressed neatly and have high-tier frequent flyer status.
Should I ask at check-in or at the gate?: Ask at the check-in desk, but the gate agent has more authority. The gate agent is the one who officially processes seat changes after the flight closes for boarding.
Is it worth buying an upgrade if I have a short flight?: If the flight is under 3 hours, probably not. Unless the upgrade gets you lounge access and priority boarding, save your money for your destination.