Bathroom light has to be switched on twice to work

We have a bathroom light and extractor fan both turned on by one pull cord, but the first time you try to turn it on, the light just flickers or doesn’t come on at all, but when you switch it off and then turn it back on, it comes on fine. We have replaced the bulb and tried a different type, but the issue remains and is consistent, so assuming something is alternating and there is a fault in one area, but not the other. Any ideas what could cause this?