Bar sink drain pump or tie into existing ejector pump

Hello all! I am in the process of adding a bar in my already finished basement. I have an existing ejector pump that a bathroom and washer flow in to currently. My question is related to the bar sink I want to add. I know I can't add a hole in the lid of the ejector pump to gravity feed my bar sink, but is it okay to core drill the concrete next to the pit and tie into the side of it? My other option is to buy a drain pump and tie into the main sewer line that runs out to my septic tank. Both options are about the same amount of work on my end. My opinion is to tie into the ejector pit - one less pump that could potentially fail. Any help is appreciated!

You can drill the side of the basin and use a rubber gromment around the pipe. You will want to buy the grommet first and ask what size hole is needed.