Is a Sole Representative's spouse who joins the main applicant later in the UK eligible to apply for ILR?
(i.e. even if they have lived in the UK for fewer than 5 years in total? Or even if they have been outside the UK for more than 6 months in each of the 5 years?)
Yes, they are. The relevant immigration rules Part 5: Working in the UK, para.196D states the requirements for dependants of a Representative of an overseas Business ("Sole Representative"), which includes a continuous period of 5 year residence. Additionally, Home Office Staff Guidance (v.13.0 April 2016) on assessing this 'continuous period of 5 years' states that no more than 180 days of absence within each year of the whole 5 years residence is allowed. While the main applicant must meet this residence requirement of continuous 5 years, there is no such requirement for their dependants.
See screen captures below. Please note this is not intended to be legal advice for anyone but general information, available on the UKVI's website. For tailored advice, please book a consultation.