I use a python monitoring script that tails logs watching for ALERT level log lines and constant order activity combined with a cron watchjob to ensure the process is alive during trading hours. The exception handler in the monitoring script sends alerts if the script itself dies.
If there are any issues I use twilio to text me the exception text/log line. I also use AWS SES to email myself but getting gmail to permanently not block SES is a pain in the ass. By design Twilio + AWS SES are the only external dependencies I have for the monitoring system (too bad SES sucks).
On my phone I have Termius SSH setup so I can log in and check/fix things. I have a bunch of short aliases in my .profile on the trading server to do the most common stuff so that I can type them easily from my phone.
I also do all my work through a compressed SSH tmux including editing and compiling code. So if things get hairy I can pair my phone with my laptop, attach to the tmux right where I left off, and fix things over even a 3G connection.
This compressed SSH trick is a huge quality of life improvement compared to previous finance jobs I've worked where they use Windows + Citrix/RDP just to launch a Putty session into a Linux machine. It's almost like finance IT has never actually had to fix anything while away from work.