I think it's very worth looking at the GIDS Evidence Base page - it has lots of very good information about the actual scientific evidence, and is from a reputable source.
Here is the link:
gids.nhs.uk/evidence-base
They have specific advice on social transition:
Social transition age
The age at which adolescents socially transition has decreased in the last decade. Steensma & Cohen-Kettenis (2011) report that between 2000 and 2004, out of 121 pre-pubertal children, 3.3% had socially transitioned (clothing, hairstyle, change of name, and use of pronouns) when they were referred, and 19% were living in the preferred gender role in clothing style and hairstyle, but did not announce that they wanted a change in name and pronoun. Between 2005 and 2009, these percentages increased to 8.9% and 33.3% respectively.
However, quantitative and qualitative follow-up studies by Steensma et al (2011; 2013) present evidence to strongly suggest that early social transition does not necessarily equate to an adult transgender identity. The qualitative study reports on two girls who had transitioned when they were in elementary school and struggled with the desire to return to their original gender role. Fear of teasing and feeling ashamed resulted in a prolonged period of stress. One girl even struggled to go back to her previous gender role for two years.
As such, in our approach, we would encourage exploration of gender roles in this younger cohort, with a view to keeping options open and not having any pre-conceived ideas as the longer term outcome.
And they have a separate page about desistance:
gids.nhs.uk/continuing-and-not-continuing-studies
There is evidence that many transgender children experience incongruence between their experienced and their assigned gender early in life (Steensma et al, 2013). At GIDS, about 15-25% of our referrals are for children aged under 12. Often these children do not identify with stereotypical behaviours and preferences of their assigned gender peers, and sometimes strongly dislike their physical sex characteristics.
In the majority of cases these feelings seem to discontinue either before, or early in, puberty (Steensma et al, 2013). In some children, however, gender dysphoric feelings will intensify during adolescence expressed by an aversion of their bodies in the context of secondary sex characteristics developing.
Across all studies approximately 16% continue with their gender identification (Steensma et al, 2013). The way gender identity develops and how gender identification is expressed seems to be influenced by biological, environmental and psychological factors (De Cuypere et al., 2013; de Vries et. al., 2014; Steensma & Cohen-Kettenis 2015).
It might be worth looking at the website itself, and examining the advice from the clinical experts alongside with the evidence base.
As I understand it, the key is for the kid to feel heard, accepted and allowed to explore who they are, and how they express themselves in a safe environment. A supportive, "watch and wait" approach is what I pick up from the GIDS advice.