You're welcome, glad you got  it fixed. 

As promised, here is the update on my " clicking " Hayter Harrier. Mick, you were absolutely correct with your diagnosis regarding the cause of the problem. I fitted the new style wiring harness, and the mower now starts every time the key is turned. I can't believe how simple it was to do the job. Thank you very much indeed for your help and advice. I really do appreciate it.

Hi Terry
Did you have any joy tracing your details. I've a similar sticker and trying to find the exact parts catalogue is not easy.
Mine has a Honda 18hp engine fitted which doesn't seem to align with anything on their list.

Unfortunately I don't,  but if I can find anything online I'll link it here.

Do you happen to have a wiring diagram by any chance?

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This company, Lupo, in Poland supply the batteries already in the casing, and they're increased capacity 2.6Ah. €20.70, a bit less than their ebay page. Shipping to Ireland €8
https://lupo-baterie.pl/en/cell-packs/102972-cell-pack-briggs-stratton-is12b-593560-108v-26ah.html.
They'll also refurbish yours to 1.5, 2, or 2.6Ah for €18.40, €20.70 or €23, plus total send and return shipping  €22.54 ( Ireland). That's a good option if you get a warrantied refurbed  battery fo half price of a new one, and no struggling  to DIY it.

Just found this thread. Excellent. I've two of these batteries, first mowing of the year, one failed completely, the other stuck on one green led. I checked that one by crossing the ground and the battery relay pin, 11.9 volts on the + terminal. I connected a 5w auto lamp, it lit for over an hour. I put the battery back on the charger and it went to 4 green leds. The other seems dead, just one flashing green led, so time to open it up. I note the difficulty with replacement cells not having spot welded tabs. I previously fixed a power drill battery with tabless cells,I managed to get a spot of solder on each battery end, but worrying in case I damaged the internals. I now see a trader who is selling the 3 battery pack and casing, reasonable price compared to a new B&S battery. Heres the link. https://www.ebay.ie/itm/23662997210
I know there are cheap LGDAHB21865 cells out there, but without tabs is a nightmare. Cells from local trustworthy sources are close to €10 each, so this eBay offering from Poland seems a good bet to restore my dud. Mower doesn't have a pull cord, so kind of stuck if I've no battery or standby

Hi Jonathan, and welcome to TGMForum.

Has it been like this for long, or just happened this year?

Is the battery good on your machine, sounds like it's just not turning over fast enough on the starter. The ignition is not powered from the battery on this engine, it actually works the other way, and spark will be cut when the stop wire on the coil goes to ground.

I would make sure the battery is good and fully charged, and battery leads have no loose connections etc.

My 725 won't start off the key. It will turn over but never fire. It will pull start and run ok.
Is this an ignition barrel fault? Maybe in tutn over position the voltage is removed from the ignition or is it a safety switch issue? Any help gratefully received
Jonathan