Be careful fitting a replacement, they are finicky to get right unless you read the manual.
I broke the switch the first time I replaced mine, many decades ago.
The later series have servos, and a switch in the engine compartment. Mine is like that, not that exact type of switch, though. Surprised the bonnet closes!
That's a breather, it lets excess air out through that hole. Just paint it up, it's fine. But you can swap to the military version with a proper breather if you want.
You need to open it up, all them bolts around the outer. Mark case both sides so it goes back in same place.
You tube "Britannica Restorations" for how to set it all back up.
But before going there can you see any welding on the bevel gears...
After you have driven it and it has played up have a feel of the ignition coil. If hot likely as @Wildefalcon says above it is breaking down. Also as @kermit_rr post replace the points and condenser.
Do you have a Temperature gauge fitted?
Here's a link to a lovely collection of a dozen Series Land Rovers for sale here in Ireland.
https://irelandmade.ie/
Just click on the Home tab on this page to get you in the right direction.....
Assuming it's petrol.
Could be evaporation of the fuel in the fuel lines.
Could be the fuel pick up pipe in the tank part blocked.
Or could be the coil breaking down.
I realise it's been a while since my last post but to put a full stop under this...
After debating whether or not to go big bucks and get a genuine Lucas relay or a blue box 'replace it in another couple of years' job i sat back and thought about...
Will try to remove the diff rear plate and check it out tommorow.
Thank you all for the help and sorry about the not so good written English, I am writting on a smartphone and it is not my native language :)