Here are a few general principles that I would apply:
Does the scale have a mix of positively and negatively worded items? If so, you'd need fewer items to identify strange cases. If it is all positively worded, then it's possible that someone could for example agree to a fairly large number of items.
Does it measure multiple constructs or does it measure a single dimension? If it measures more than one dimension (e.g., like a five factor personality test), then you'd expect to see more diversity in responses.
From first principles, it can be helpful to consider whether there is any conceivable reason to provide such a sequence of responses that would reflect conscientious survey completion.
You may also want to think about your survey design and the incentive structure to consider what incentives there are to respond in given way. Some survey designs make that mode of responding more efficient.
Another general strategy is to calculate an index and plot the distribution of cases on that index. If you see a break in the histogram, this can suggest that a discrete process (i.e., non-conscientious responding) has caused the data on the other side of the break. This can be helpful when looking at things like survey completion times. In the case of providing only one response option to a set of items, you can obtain a count of the number of response options and tabulate and look to see whether the vast majority provide all the responses. Alternatively, if it looks like a common response type, then you'd be less likely to conclude that it is problematic.
Here is one way to get this in R assuming
data is your dataset and
items is a vector item names.
data$unique_responses <- apply(data[,items], 1, function(X) length(unique(X))