It will depend on the midwife, in my experience. I had continuous monitoring with my DS (first baby) as I was induced due to being overdue and was told that whether I would be "allowed" to move around would depend on the midwife on duty
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As it was, the midwife I had was very old school and insisted that I be on my back on the bed. Given the monitors and the drip, blood pressure cuff, etc, I couldn't even turn onto my side without assistance and she was unwilling to help until I insisted as it was just too uncomfortable. I was also not allowed to the toilet and had to use a bedpan.
I was in the same position for 7 hours and it was awful, I'm not going to lie. I think it played a significant part in why I ended up with an EMCS for failure to progress. Baby was not in distress at any point, but she was very concerned that anything other than being immobile on my back would interfere with the equipment.
The next midwife positively encouraged me to move around as much as I could, ie to be upright, on a birth ball, or in any position I found comfortable that they could monitor me in, and to use the loo. This was more manageable.
I'm not qualified to say whether you should refuse continuous monitoring in place of intermittent, but I would say that continuous monitoring could have an impact on your labour depending on how it is managed. I would encourage you to think in advance about your options and what your red lines are. It depends so much on the midwife you get and how comfortable you are challenging/asserting yourself in that kind of environment, and whether your birth partner will advocate for you.
My personal view is that next time, I will be having an ELCS because I couldn't cope with continuous monitoring if I had to be on my back. But that's me, not you, and you might well feel it was a price worth paying for giving VBAC a go.