Generally I have found Cathay flags their discount codes on the website, it isn't a super secret "sale", as if they did that all of HK & the rest of China would likely know in about 10 minutes thanks to the various bloggers. Here is an example with 25% off using a promo code for 3+ seats to give you a flavour of what it can look like:
https://flights.cathaypacific.com/en...ion-offer.html
However, most Cathay sales and promotions are fairly date, route, and class limited - with the exception of their Vantage (two business returns to different locations for about the price of one if booked together - so you get a significantly discounted medium or short haul flight). Best that you track via google flights and see what happens, and sign up to the Cathay newsletter from your origin.
Since you say January 2026 I presume you are avoiding both Christmas and Chinese New Year (late February in 2026) so there wouldn't be any specific reason to buy until a general sale - but this isn't Qatar / British Airways, there aren't regular multi-digit discounts, or lots of promotion codes for things like Visa/Mastercard/App purchases hanging around most of the time.