First, you have an Iron Barrel. It is called that because, like the Bullet's dating all the way back to 1935, it has an iron cylinder that the piston runs up and down in.
The newer AVL or Lean Burn and the new Unit Construction Engine (UCE) engine has a more modern aluminum cylinder with a steel liner.
People nicknamed the old engine like yours an" Iron Barrel" partially out of affection and partially because it is quite different from the newer type engines so it has its own set of answers to questions about it.
The blinker relay most likely looks like a small black box approx 1" X 1" X 1" (25mm X 25mm X 25mm) in size.
If you replaced your indicator's, did they have 2 wires or were they like the chrome plated steel bullets I used on mine which only had 1 wire?
The kind like mine which only have 1 wire use the body of the indicator as the ground path.
That should make connecting them pretty easy but it doesn't.
First, the body of the indicator must contact bare steel on the frame. An alternate idea is to install a dedicated ground wire that contacts the body of the indicator.
Another problem is, the two wires that connected to my old indicators were not what they seemed to be on my 2011.
The wire I thought was the ground wire turned out to be the power wire and the wire I thought was the power wire turned out to be the ground wire.
When I hooked up my indicators I basically wired the power wire directly to the housing which was grounded to the frame with the mounting nut.
To find out if this is your problem you will need a Volt/Ohm meter. They measure voltage and resistance and can be bought for about $8-$10 at a Harbor Freight store or about $20 at a large hardware store.
To use it, set the selector to Ohms (looks like the Greek letter Omega). Turn it on if it has a switch and touch the two test wire tips together. The reading should be 0.000 (zero). If it is working, now touch one of the VOM's test wires to one of the wires that comes from the harness to the indicator.
Holding this in contact, now touch the other test wire to some bare part on the motorcycle.
If you get a reading of zero or close to it, the harness wire you connected to is the ground wire.
The other wire is the power supply wire. Make sure the power supply is the one that connects to the rear of the bulb in the indicator.
By the way, having a good VOM is a real good idea.
Royal Enfield's can develop all sorts of issues with their wiring and having a VOM can let you figure out what and where the problem is.