Adding a second 12 power converter to a 36V electric cart

[Lmathies]

Hi, I have a 12V power converter on my 36V golf cart for the lights which is activated by the "light" position on the key switch. I want to add a second 12V power converter that will activate with the "ON" position on the key switch for a radio and phone charger. Can I connect a second 12V converter to the battery pack or is running two 12V power converters off of the same 36V battery pack not a safe thing to do?

Thank you in advance.