Logically, the TG stands for "Tyddyn Gwladys" SH 735266 which is usually regarded as a gold mine, however the lodes also carry galena and sphalerite. According to Foster Smith it was not worked for these minerals after 1862, however Dewey and Smith (BGS Memoirs) regard galena as the principal ore.
From what you have posted there is a 'gold' connection.
There are about 10 mines in the Trawsfynydd area, some only trials, but most principally for copper or gold.
Addition
Yes I was right. Tyddyn Gwladys Silver Lead and Gold Mining Co, £30,000 share capital in £1 shares. George Williams manager, also managed Dolfrwynog. Replaced by Ezekiel Williamson. At Dolfrwynog he was criticised over his drink problem by one of the shareholders, and was discharged in 1864. Also blamed for the lack of success of the mine. Sorry.
Ref. The Gold Mines of Merioneth by George Hall, pages 41 and 42.
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