No, you can not safely upsize the fuse in an existing circuit. The fuse in a circuit is typically selected to match the current carrying capacity of the wire gage in order to protect the wire from burning up from excessive current draw.
American Wire Gauge table and AWG Electrical Current Load Limits
The trigger lead 86 of a typical Bosch 30 amp relay is very low draw, less than one amp, and could use a small gage wire and tap an existing circuit that is switched by the ignition. When the trigger lead is powered, it energizes coils in the relay which pull the contacts closed, connecting the power in 30 to the power out 87. The inside cover of the passenger side dash fuse box has the circuits marked IGN or BAT and indicate whether they are powered directly by the battery or switched by the ignition. You could tap an IGN circuit with a littlefuse mini-blade add a circuit or a Radio Shack fuse tap and run a small gage wire through the A/C drain grommet to a relay under the hood for the trigger wire. Alternatively, there is probably an IGN on circuit you could tap in one of the fuse boxes under the hood.
It is not clear to me how the lighting circuit is connected where it indicates +Light on the diagram. Is that connected to a switch or do the lights stay on all the time?