Which wires to new switch

One year ago I fitted some new LED auxiliary lights to my 2015 R1200RT. I purchased the after market lights off Amazon for about £55.00. The kit consisted of a pair of LED lights, wirering harness, relay and on/off switch. Lights have worked fine as they should.
However the original switch is corroded inside, not waterproof, so I have purchased a new waterproof on/off motorcyle switch, and now my puzzle begins.

The original switch has 3 spade connections on rear connected to the wiring loom:
One (yellow wire) to the trigger wire which becomes live only when the ignition is on.
One (black wire) connects to 86 on the relay.
One (white wire) connects to 85 on the relay.

The new switch is pre-wired into rear of switch(3 wires about 400mm long)with instructions stating where the wires are to be connect to:
One Blue wire. (connect to the equipment positive).
One Brown wire. (connect to Negative).
One Black wire. (connect to Positive).

I have no idea how this all works and don't like to mess with electrical stuff.

To avoid any electrical damage...Can anyone please advise which wires (blue,brown &black) on the new switch...... connect to which wires (yellow, black & white) on the loom connection?

I'm guessing the switch is something like this one ................. https://www.amazon.co.uk/Motorcycle-Handlebar-Waterproof-Headlight-Indicator/dp/B07H9YQFMV

The connections to the relay & accessory will follow the usual pattern ......... https://www.delcity.net/documents/automotive_relay_diagram.jsp

Connect your ignition live wire to one side of the switch.

Connect the other side of the switch to terminal 85 of your relay.

Connect terminal 86 of your relay to earth.

Run a cable from your battery +ve terminal with an inline fuse to terminal 30 of your relay. This wire has to carry the load for the LED lights. Make sure it is thick enough. Locate the fuse as close to the battery as you can.

Run a similar sized cable from terminal 87 of your relay to the positive of the LED lights.

If your relay has a terminal 87a, insulate it.

Run a cable from the LED negative to earth.

Keep the cable runs near and use plenty of cable ties. Flapping cables will cause issues later.

Job sorted,
New switch wires:
Black wire connect to yellow wire, (trigger switched ignition).
Brown wire connect to black wire, which connects to pin 86 (ground) on relay.
Blue wire connect to white wire, which connects to pin 85 on relay.

Lights work now.

Many thanks for your help.