The LED light draw so little current - they fail to get the stock mechanical blinker "stimulated".  The stock flasher unit has a "bi-metal" strip that heats up from the current passing through......the metal heats up and breaks the circuit, then cools down and completes the circuit....and this repeats until you cancel the signal.  The LED does not create enough current to heat up the metal strip in the flasher.

You need to buy a solid state or eletronic flasher relay.

Any 2 prong electronic relay will work - however some will allow you to use the stock Suzuki connector.

The flasher relay is on the right side of the frame, under the fuel tank, almost directly opposite the ignition coil.  It is a small cube held on by a rubber mount.

This claims it fits the Savage.
https://www.customled.com/products/elfr-1-electronic-led-flasher-relay