Yes, you need to provide constant 12 volt power. Normal charging modes on tenders don’t do what you need. For example, when you go to CTEK, Mercedes choice, you need to go to their 7002 series which provides both charging and direct power capabilities. And … there are a few other things you should do, make sure all power consumers are turned off, put the driver window down, put the key at least 3 meters from the car and don’t try to use the cigarette lighter as a plug-in because with the ignition off it’s not connected to the system. Use either alligator clips on the terminals under the hood or an OBD II connector.
I’m not sure about the age of the battery from your description but for what it’s worth, I change both batteries and tires at 5 years regardless of mileage. Haven’t ever had to hitchhike.