I am unable to follow the hearing as closely as I would like. I haven't been able to read the reports of the last couple of days. However, my thoughts (and apologies that the first one is a repeat of something I said on the last thread, but I think it is important to be clear on this)...
Although SEEN is only an intervenor in this case, if the outcome places them at a disadvantage they should be able to appeal. Indeed, even if they were not a party to the proceedings at all, they would be able to appeal if they could show that they are directly negatively affected by the judgement, or that their legal rights have been affected.
If it has been correctly reported, the decision of the tribunal to prevent NC and a witness from using biologically correct pronouns for the claimant is astonishing. The Equal Treatment Bench Book says, "Witnesses should never be compelled to use the trans person’s preferred pronouns". Whilst the judge does not appear to have gone quite that far, allowing NC and her witness to use neutral pronouns and the claimant's name, this is definitely pushing the limits. It may give rise to two possible grounds for appeal if the decision goes against SEEN in that it could be argued that this ruling gives an appearance of bias, and it potentially makes it difficult, if not impossible, for NC to present SEEN's arguments properly.
As with previous cases, this case will see GI witnesses making statements that are clearly nonsense. If you want to understand why apparently intelligent people say such things, I would recommend reading Why Smart People Believe Stupid Things - by Gurwinder which explains the concept of Fashionably Irrational Beliefs (FIBs) and why intelligent people cling to them.