what size/kind of capacitor is needed 12VDC automotive
The bottom part of your diagram will not work with the way you have placed the capacitor. Below you will find a better diagram of what might work. The 2 second delay greatly depends on amount of current the relay takes. You will likely need a big capacitor with this diagram. 







simulate this circuit &ndash; Schematic created using CircuitLab

If you add an NPN transistor as amplifier you can use a much smaller capacitor. Also the load on the indicator driver is much lower thus your indicator circuit is very likely to work normal.







simulate this circuit

Both of these are principle diagrams. I am afraid for details we need to know more about the NO relay in your picture.