Thank you for the response.
I'm attached an image to show how it displays without the CSS override. In the image I first attached you can see that the scroll bar is present, but it isn't clickable. I can however select an item, open the dropdown again and use the arrow keys to get to the items further down the list.
The additional setting of the height you posted doesn't affect the time picker, but does affect the general drop down list control which I have used elsewhere.
Here is a snippet of the column bounding within my cshtml file:
cols.Bound(e => e.StartTime).Groupable(
The "Time" editor template file:
@(Html.Kendo().TimePickerFor(m => m)