Taiwan has had the same struggle as mainland China, when it comes to vaccinating old people.
First of all, mainland China's numbers are similar to those of Taiwan. As of March 2022, 82% of people aged 70-79 in China had two shots, while 51% of people aged 80 and up had two shots.[0] These numbers have probably come up a bit since then.
Second of all, Taiwan has a similar curve of vaccination rate vs. age. In Europe and the US, vaccination rate generally rises with age. In mainland China, Taiwan and Hong Kong, it's the opposite, and quite dramatically so.
Source: https://covid-19.nchc.org.tw/dt_002-csse_covid_19_daily_repo...