Opinion

Fugitive WHO? 

Most people were not warmly receptive to the Timeless Child arc or the fact that Ruth/Fugitive Doctor's Tardis looks like a police box. I have even seen comments like- after this, the WHOLE of Doctor Who has been spoiled due to error in continuity. But that is essentially not true. Considering that Ruth is pre-13, is it really that impossible to believe that the same person in their own previous incarnation had the same instincts. Despite this story being in the same or an alternative universe, maybe before settling in Gloucester and activating the Chameleon persona of Ruth Clayton, the Doctor did a recon of the area first in late or mid 70's, where she instinctively thought it would be a good camouflage to keep the Tardis hidden as Police Box. Then due to some rushed judgement maybe it stuck that way. Nowhere does it say that Ruth has a Tardis with a faulty camouflaging mechanism as well. Maybe she CAN revert back.

Plus seeing the design on the Tardis interior, my headcanon is that she is pre-Hartnell, with probably a Type 40+ TT capsule issued by The Division or a body like the Celestial Intervention Agency (C.I.A), which she instinctively turns into a telephone box. After her memory loss the First Doctor chooses his faulty Tardis that he steals to instinctively remain the same way. Is it the same TARDIS OR NOT, I DO NOT KNOW.

Plus I LOVE the Timeless Child arc cause it opens up potential doors to the return of the Valeyard. The Valeyard, as said by the Master, was between his 12th and last versions. Maybe the Timeless Child reveal and subsequent stories is what sends a version of the Doctor off the edge. Plus it also explains THAT The Brain of Morbius Scene. 

 Lore says that the 1st Doctor had a Type 50 TT Capsule that he left in a hurry, in Gallifrey, before stealing a faulty Type 40. Maybe the Ruth Doctor has a Type 50 or Division Issued Military Tardis (Not a 'War Tardis').