It's an on/off push button switch.

It's used to power on and off the E bike.

The ebike seems to be on all the time.

I suspect the switch, but it does mechanically switch on/off with a small 'click' and the on position is down at it's bottom travel end and off at the switche's near top travel.

The switch has 4 terminals.

The green switch light is on all the time.

I'd like to buy another switch and test it.

more than likely dust, give it a spray with lubricant WD 40

21 minutes ago, sometime said:

more than likely dust, give it a spray with lubricant WD 40

Thanks. Trouble is WD40 sprayed terminals attract more dust later on. 

A million years ago when I used to work with telecom relays, the report was that spraying relay springsets with WD40 caused more intermittant problems later on.

Seems you are looking for some like this

 

https://shopee.co.th/สวิตช์ปุ่มกดไฟ-LED-กันน้ํา-19-มม.-พร้อมเครื่องหมายพลังงาน-5V-12V-24V-i.596128542.21611071127

1 hour ago, sometime said:

more than likely dust, give it a spray with lubricant WD 40

As has been mentioned WD 40 is not correct, in fact it is almost the absolute worst thing to use. 
first a contact cleaner, this is an example 

 

break clean may also be OK

then if actually required a dry PTFE maybe needed, but clean dry contacts are what was designed to me used.

Go to any MR DIY Store, Contact  Cleaner 79 baht, I use it as brake cleaner as its cheaper.

Has it ever worked as you expect it to and has now stopped?

 

Have you checked that the switch is actually off when it's in the off position (clicked out)?

 

The switches linked to by @UWEB look promising but you need to verify the actual contact arrangements on your switch.

9 minutes ago, Crossy said:

Has it ever worked as you expect it to and has now stopped?

 

Have you checked that the switch is actually off when it's in the off position (clicked out)?

 

The switches linked to by @UWEB look promising but you need to verify the actual contact arrangements on your switch.

I'm in the process of checking out the switch but there are a lot of wires, fairly stressed, in a small area, so I'm going to have to discharge the battery first. 

The battery and taillight are 1 unit that slides into the bike frame. The taillight is on all the time regardless of state of battery press button.

The digital display seems to have power all the time (switching the display on/off still has backlight and functionality).

Maybe the press button switch is underrated, not being 48v rated?

12 hours ago, UWEB said:

Seems you are looking for some like this

 

https://shopee.co.th/สวิตช์ปุ่มกดไฟ-LED-กันน้ํา-19-มม.-พร้อมเครื่องหมายพลังงาน-5V-12V-24V-i.596128542.21611071127

Thanks. I'll have to check more but the bike has 48V Samsung batteries so the switch may be underrated.

I have 2 of the same ebikes and both now have their taillights on.