Don't get distracted by clutch-switch, it's fine. Both start-button and clutch-switch are in series and both must be operational to activate starter-solenoid. IF one or other is defective, you'd get zero action whatsoever, no click, no lights dimming, nothin'. Since you get lights dimming when pushing start-button (activating starter solenoid), both switches are working. Problem is dead battery.
Fact that lights dim shows that only problem is dead battery. ALL you need to do to verify bunk battery is this test. Gets you answer in less than 5-minutes and you can be on way to fix bike.
1. measure battery power with everything OFF, VOLTS=???
2. measure battery power during cranking, VOLTS=???
For reference of "normal" and "working" battery, here's my battery-voltage on VFR after 4-months winter storage (lithium, no battery-tender needed).
Turn on key for 10s and wait for pump to prime carbs. Push start, spins for 2-revolution and >VRRROOom<
Some related posts with people resistant to measuring their battery. As soon as they do it, they find problem and bike is fixed in 5-minutes. Or less in many cases. Make note of test and measured numbers.
https://www.ninjette.org/forums/showthread.php?t=368961 - jumpstart test confirmed
"
Hmmm... doesn't feel like battery." - batteries have feelings???
https://www.ninjette.org/forums/showthread.php?t=335199 - 13.6v
"So I checked the voltage when starting and the battery dropped to 2 volts."
https://www.ninjette.org/forums/showthread.php?t=74813
"There is power because all the lights come on but as soon as i press the starter button
it clicks and then the power goes away for a minute or two"
https://www.ninjette.org/forums/showthread.php?t=61661 - charging fixed
https://www.ninjette.org/forums/showthread.php?t=113945
" Then I noticed ALL the indicator lights were dead."
https://www.motorcycleforum.com/threads/battery-problem.95559/#post-634109
https://www.motorcycleforum.com/threads/new-battery.122626 - 14.21v
https://www.motorcycleforum.com/threads/starting-problems.80408/#post-485100
"well i charged the battery and shes ok now, thank god"
https://www.mvagusta.net/threads/bi.../threads/bike-wont-start-battery-voltage-12-52-really-not-enough-voltage.41789/
Numbers tells exactly what's wrong and how to fix it in less than 5-minutes. I can see trend with voltage-drop getting larger and larger as battery wears out and I can replace before it leaves me stranded. I've had case of bad battery that starts bike fine to go to filing station
*. After adding petrol, I get ready to go, push start-button >CLICK<, lights dim, nothin'... Similar to what you were experiencing earlier. These are signs of battery going downhill...
PS It was working well before (with an occasional lack of engagement), yesterday fine, but today nada.
----------------------------------
*There was conspiracy theory that this filling-station had dark-tech that was killing batteries. Many, many people reported that their batteries died right after filling tank there. There was cell tower across street but research is still out on them contributing to EMF related diseases. Battery is high-power DC device, I doubt cell tower can hurt them. Lack of measured quantitative data can lead to all sorts of wild theories on cause & effect.
I asked attendants of station if they noticed any larger rate of moto batteries dying than autos, which they couldn't say one way or other. Just batteries dying for both autos and motos. Looking on map and at online meet schedule, I suspect real cause was higher-rates of motos stopping there to meet up for rides than other stations. It was just at edge of town right before popular mountain twisties. It had plenty of space for waiting motos. Low cost of petrol relative to other stations in town. With more quantitative data such as numbers of riders per day, I'm sure trend would appear to pinpoint actual cause.
Again, gather quantitative numerical data and post them here. Is easiest and fastest way to fix electrical problems.