The lights by the right eject chute flash for the first ball eject after the game is switched on, then stay dark on every later eject while the ball still kicks out normally. Power cycling gives one more flash.

Right chute lights flash once after power-up, then never again: bad lamp socket

Cause: A bad socket on one of the right chute lamps.

Checks

• Swap the bulbs to rule them out.
• Check the chute switches in switch test.
• Inspect each chute lamp socket for a loose or corroded contact or cracked solder, and check its wiring.

Fix

• Repair or replace the faulty lamp socket.

Systems

• Williams System 11

Games

• High Speed

Related tips

• Pop bumper, sling and right-side GI lamps all go out at once: blown GI fuse
• Right-side playfield GI out: a wire not seated in a new power board connector
• LED flashers glow or stay on: use bulbs in System 11 flasher sockets
• Part of a lamp row or column stays off
• Flash lamp dead on an early System 11 game
• All CPU-controlled lamps out
• Single matrix lamp out with good bulb and wiring
• Lamp lights twice or two lamps act as one

Source: Pinball Repair help group!! (Facebook group)