I don't use TailScale but it's probably due for an update. Beyond that there may be a script that needs tweaking or an addition to your /etc/rc.local or crontab. If you're using Ubuntu then you should translate that cronjob to a SystemD .timer:
Hi there [asciicast]
An alternative way of enabling the exit node mode without editing the start script or running frequent cron commands.
Go to Lucy then System->Startup->Local startup
Enter above the exit 0 line:
( sleep 60; tailscale set --advertise-exit-node ) &
This will allow the router to start all processes, including Tailscale connection and, after 60s, will set the flag --advertise-exit-node.
This solution persists after the router updates.
It’s probably not the most ideal solution but I have the following scheduled task in LUCI scheduled tasks.
*/1 * * * * sudo tailscale up --advertise-exit-node --advertise-routes=192.168.1.0/24 --snat-subnet-routes=false --accept-routes