Bit confused of your requirements .
If you are working/contracting for highways England just parking a car in a TM/TTM closure requires a bit more than parking lights left on , and excerpt from Section 8 regulations 2006...
The new Chapter 8 now says:
Without prejudice to the specific requirements of the following sections, any vehicle stopping on the highway for works purposes or inspections shall be equipped with either a roof-mounted amber warning light bar (comprising at least two independent light sources) or two independent roof-mounted amber warning beacons, visible through 360°.
O5.3.2 Warning beacons must comply with the requirements of the Road Vehicle Lighting Regulations and should also comply with the United Nations Economic Commission for Europe (UNECE) Regulation 65 on
Special Warning Lamps.
O5.3.3 If the main beacon is likely to be obscured from the rear by parts of the vehicle or any equipment
carried on the vehicle, additional beacons should be fitted toward the rear of the vehicle where they will remain visible.
O5.3.4 The beacons shall be in use when entering, leaving or moving within the site, when travelling in traffic at less than the general traffic speed, and when stationary on the hard shoulder.
O5.3.5 When stationary within the confines of a fully installed traffic management arrangement, the beacons shall be switched off, unless they form part of the guarding of the works, e.g. works on minor roads, or are required for mobile works; see Sections O10 and O11.
I am not in this trade but one of my mates owns a very big TM company and I have a number of friends who work on 'the motorways' and even the few who do not use vans have the regulatory yellow reflective stripes on their saloon cars 'motorway maintenance' and chevrons stickers on the rear.
Otherwise they are not allowed to enter the closure. Your circumstance might be different , must admit before I met these blokes I always wondered why I would spot boggo passenger cars with all this stuff stuck all over them .